1.Introduction 3 2.Deriving general expression of Numerator 3 I.Using Pattern Recognition 3 II.Using Progression 5 3.Deriving general expression of denominator 10 I.Using Pattern Recognition 10 II.Using Progression 11 4.Validating the general expression 14 5.FINDING ADDITIONAL ROWS USING GENERAL EXPRESSION 19 6.Conclusion 36 7.Limitations 36 1. Introduction Lacsap's fractions are based upon Pascal's triangle. The general triangle's rule is "Starting with1/1 at the top, the numerator (top number) is increased by one each step to downward right, and the denominator (bottom number) is increases by one each step to the downward left. Each fraction on the inside thereby has the numerator of the fraction to its upper-right, and the denominator of the fraction to its upper-left." So basically, going to the right, the denominator increases but if we go to the left, the numerator increases, both by one. The purpose of this assignment is to examine a set of fractions presented in a symmetrica

Carl Jung, a Swiss-German psychoanalyst, developed several theories of the unconscious and was instrumental in bringing psychology to the 20th century. He was born Carl Gustav Jung on July 26, 1875, his family was well educated and included clergymen and eccentrics. Freud and Jung together and alone contributed greatly to the development of psychology. They worked together and corresponded many times, they had different views and adopted unique theories of their own - Jung's of mythology and Freud's theories on sexuality. While both had ideas on personality , Freud is known for labeling the id, ego and superego; the id, with its goal of immediate pleasure, the ego which is based on the reality principle and the superego, containing values and morals (Boeree, 2000,2006). Jung saw the ego as the conscious mind, akin to personal un

?Who I am today was molded by my family, friends, religion, customs, and traditions. All of these played a role in creating my beliefs, ethnics, and character. These traits are what make me the person I am today and will be tomorrow. I was born in Liberia and my family moved to Cote D" Vore when I was six. When I was eleven, we moved to the United States (Providence, R.I.) I grew up in Providence, Rhode Island with my aunt (Gormah Karmue) and was one out of 5 children. At an early age in my household we were taught to work for what we wanted. My father died when I was three years old which impacted my family greatly since my mother could not afford to take care of my four brothers and I back in Liberia, especially in a war zone. So this is the reason why I grew up with my aunt. Our first two years in the U.S. we were living on warfare because my aunt was not use to the American system and because we had get all of our paper work situated to be in the U.S. and to work. After scho

People have different languages and accents around the world. As a matter of fact, people can even speak the same language yet have a different accent. Everyone sounds different; whether they are from a different country, different state or even a different city, everyone has their own accent. For my investigation I have chosen a person that speaks English but is from another country. Navin Poon is a Guyanese/American college student, who is 18 years old. Although he was born in New York, his parents and extended family were born in Guyana. He lived with both parents and his two older brothers in their house in Jamaica, Queens while growing up. Navin was surrounded with his grandparents, aunts, uncles, cousins, and of course friends and neighbors that were also Guyanese. Being surrounded by these people during

Introduction In his 1962 essay, "Canada's Long Term Strategic Situation," Dr. R. J. Sutherland took the unusually bold step of predicting the stable foundations of Canadian defense policy for the next four decades, even though he was writing at the height of Cold War tensions and amid revolutionary developments in nuclear weapons technology.1 An economist, cavalry officer and operational analyst with experience of World War Two and the Korean conflict, much of Sutherland's work for the Department of Defense remains classified and although his career was cut short by his untimely death in 1967, aged only 45, he is considered by many to have been "Canada's preeminent strategist of the 1950's and 1960's".2 Sutherland was working for Canada's Defense Research Board when his seminal essay on Canadian security was published in the International Journal. Despite the dramatic global changes since "Hitler's War", Sutherland argued that the very concept of national security required consisten

Task 55 Describe in your own words what the following eating disorders are and what the needs of the individuals suffering these disorders are; anorexia, bulimia, binge eating Anorexia Nervosa Anorexia means 'loss of appetite from nervous origins' suffers say that they do not feel hungry, though recovered sufferers do admit that they were very hungry, but did not allow themselves to eat. When a person suffers with this condition they become fixated on their body weight and dieting. They live in fear of normal body weight so are continually pushing themselves towards becoming thinner. Sufferers of this condition can be fanatical with food but they will refuse themselves healthy meals and follow strict diets to make sure they lose as much weight as possible. Anorexia sufferers do not think that there is anything wrong with the amount of weight they have lost even when others see them as being extremely thin. People who have anorexia often have very low self confidence and f

Buddhism and Hinduism are two of the most influential and profound religions in the world. Both denominations originated in India, therefore, possessing many similar ideas and philosophies. They have existed for many centuries and are still widely practiced religions today. Buddhism is based on the ideas and teachings of Gautam Buddha, who was once a Hindu before becoming a Buddhist because of Hinduism's "complex nature." Buddhism and Hinduism share many similarities as well as differences due to their ethical beliefs and philosophies. The followers of Hinduism and Buddhism both live their lives every day based on the teachings of their religion. Reincarnation, the concept that the spirit after death begins a new life as a human, animal, or other being based on the moral quality of the previous life's actions, plays a big role in both religions. Hindus follow the concept of reincarnation because they believe if a person does good deeds throughout their life, then they will be reincar

American's are over medicated. People are looking for a quick fix to their problems and often turn medication to make them feel better. In some cases there can be a quick fix, for instance, taking a Tylenol or an Advil to relieve a headache. But in other cases, that quick fix can turn into a quick problem. Addiction to prescription medicine is becoming an epidemic - taking over people's lives and ruining relationships. Other than addictive drugs, direct-to-consumer advertising is becoming an issue for debate. Consumers are being manipulated into thinking the pill being advertised is the answer to all their problems. This causes viewers to self-diagnose themselves and demand commercially advertised drugs from their doctors even though they may have no medical training. These drugs and the associated advertising should be regulated to prevent further addiction, abuse, and manipulation by pharmaceutical companies. The amount of prescription drugs flooding our nation is becoming an epidem

?Setting - Three theorists arrange a meeting at an undisclosed location to take part in a lively discussion regarding the recent addition of Youth Justice Conferencing as a sentencing option in the Criminal Justice System. Durkheim: Good morning Lombroso. How are you this fine morning? Lombroso: Fantastic. Would you believe I actually just finished reading your interesting theories in The Normal and the Pathological last night. (Durkheim, 1985). Durkheim: Oh really? I take it by your response you however disagree with some of my views? Lombroso: Overall, you have formed a strong perception, however yes there are some aspects I don't agree with. Beccaria: Sorry I'm late. How have you been Durkheim? Durkheim: Very well. I'm assuming you know or are familiar with the work of Lombroso? Beccaria: Lombroso it's been awhile. I have to say your insight on criminality is extremely captivating. The facts that you presented in The Criminal Mind (Lombroso, 1911) are quite intriguing. Lombroso: W

?The Suez crisis was a conflict that could have easily turned into a third World War. With a battle between the Israelis and Egyptians at Sinai, the British and French invasion of Egypt, and nuclear threats from the Soviet Union, all of the elements were present to escalate the conflict and pull other countries into the fray. Canada had no direct ties to the Suez crisis, in terms of control or economic interest. However, Canadian Secretary of State for Foreign Affairs, Lester B. Pearson, persuaded the UN General Assembly to send in the United Nations Emergency Force. Even though Lester B. Pearson dismayed the Commonwealth with his measures for peace, Canada was recognized for starting the first ever United Nations Peacekeeping mission. In the 1950's the Middle East was affected by four different conflicts; each one separate, but relating in many ways. The first was the rush for geopolitical dominance between the United States and the Soviet Union during the Cold War. The Middle Eas

?Table Of Contents Abstract 2 Keywords 2 Abbreviations 2 Literature Review 3 Thesis 5 Introduction 5 European Union 5 Turkey 7 Problems That Affects Accession Process 6 Sovereignty Problem 6 Cyprus Problem 6 Minorities and Non-Muslims Problem 6 Conclusion 7 Reference 7 __________________________ Abstract: The aim of this study is to help people decide whether membership of Turkey in the union is profitable or not for European countries. Since there are so many thoughts about this issue, it is very hard to make an objective decision. In order to make an accurate decision, graphs and data are collected from credible sources. This paper represents both negative and positive ways of the membership by the helps of figures and statistics. Keywords: European Union, Turkey, membership, Cyprus. Abbreviations: EU - European Union ABGS - Avrupa Birli?i Genel Sekreterli?i EUROSTAT - Statistical Office of European Union Thesis:

Factors Leading up to the Fire On October 8th through October 10, 1871, the city of Chicago was the site of one of the greatest, most destructive conflagration fires of the 19th century. Every factor predicating such an event was present. The city was going through a severe drought, the fire department was fatigued and over worked, and strong winds were present. Theory of the Origin of the Fire There are many theories regarding how the fire began. Some say the first spark was in Mrs. O'Leary's barn on the night of October 8. The most popular legend is that Mrs. O'Leary's cow kicked over a kerosene lantern in her barn, causing the wooden framed structure and its contents to catch fire. Another theory points to a local man who may have accidentally started the fire when his pipe blew a spark in the O'Leary's barn while he attempted to steal milk. The initial event of what caused the Great Chicago Fire or who (or what) was truly responsible may or may not ever be known, but but the devastating outcome of the fire cannot be denied. City officials estimated

Factors Leading up to the Fire On October 8th through October 10, 1871, the city of Chicago was the site of one of the greatest, most destructive conflagration fires of the 19th century. Every factor that would predicate such an event was present. The city was going through a severe drought, the fire department was fatigued and overworked, and high winds were present. Theory of the Origin of the Fire There are many theories regarding how the fire began. Some say the first spark was in Mrs. O'Leary's barn on the night of October 8. The most popular legend is that Mrs. O'Leary's cow kicked over a kerosene lantern in her barn, causing the wooden framed structure and its contents to catch fire. Another theory points to a local man who may have accidentally started the fire when his pipe blew a spark in the O'Leary's barn while he attempted to steal milk. The initial event of what caused the Great Chicago Fire or who (or what) was truly responsible may or may not ever be known, but the devastating outcome of the fire cannot be denied. City officials estimated that more than 300 p

The novel, "July's People" by Nadine Gordimer is about a white, liberal South African family, which is forced to escape from Johannesburg to the native village of their black servant, July. The Smales family are hosted by July`s village and for their survival, they must depend on them for everything they need. July is the leader of his village and the Smales family come to appreciate July as a compassionate, intelligent human being rather than just a servant. I will elaborate on the growth and evolution of Maureen and how it is traced in the novel, "July's People". The lives of the Smales family changed dramatically when they were forced to flee Johannesburg and take refuge with July and his people. The Smales had been the epitome of "white society of colonialism" in South Africa, but now, their lives were turned upside-down; their servant had become their master. July stepped in and provid

The U.S government and the media have a reputation of blowing things out of proportion. They make can cause society to become fearful and afraid of the outside world. In 2009, the United States had a wide-spread pandemic of the Swine Flu or the H1N1. The H1N1 was a type of influenza that was different from a typical flu. When H1N1 hit the U.S, people made a big deal of it because the reaction it had on the government and media. On August 10, 2010 the World Health Organization (WHO) International Health Regulations (IHR) Emergency Committee declared an end to the 2009 H1N1 pandemic. Now it is just considered a regular "seasonal influenza" virus (CDC.com). When the H1N1 hit the U.S. and people were diagnosed to have the swine flu many people panicked because there was no vaccine for it. It became a near pandemic because the U.S government declared swine flu to be a public health emergency and above that, The World Health Organization considered it a global emergency. People

?The text under interpretation is a short story called "The Wind Blows" written by Katherine Mansfield. Katherine Mansfield was a prominent modernist writer of short fiction. Her life and work were changed forever with the death of her brother during The Great War. She was shocked by the experience so much that her work began to take refuge in the nostalgic reminiscences of their childhood in New Zealand. Her stories were the first of significance in English literature to be written without a conventional plot, she concentrated on one moment, a crisis or a turning point, rather than on a sequence of events. The plot is secondary to mood and characters. Speaking in terms of functional stylistics the text under consideration is a bright example of belles-lettres style, the main aim of which is to suggest a possible interpretation of such phenomenon of life as growing up. The text under interpretation represents the genre of a short story, which can be proved by such features as disjointed timeline, limited number of characters and an abrupt opening. The given text concentrates on a single emotion of becoming mature, which is implicitly revealed to the r

The first president of the United States, George Washington, left office with one of the most powerful farewell speeches ever given. He continued to counsel the country during his departure from government. Washington warned the country about detrimental proceedings in government such as establishing permanent alliances with other countries; and shared his belief that political parties were harmful and divisive and could, therefore, tear the nation apart. George Washington had every right to believe that political parties would divide the nation - and he was right - that is exactly what is happening today. Two-hundred and fifteen years later this country has become the complete opposite of wh

?Step One Identify The Decision To Be Made The goal of my portfolio is to decipher more about myself than ever before. I would like to find out about the different qualities that make up me, because through this knowledge I can figure out what career path would best suit me. I already know that I want achieve success within my career and I want to be comfortable and happy with myself throughout my life. I want to achieve success because being happy and comfortable with myself are the most important things in life. I also want to be proud of my accomplishments. I don't want to be angry with myself because I wish I had tried certain things but I did not. So, for me success is the answer and the key to making and educated decision as well as a rational one for a career choice. The only way to achieve success is through planning ahead. I know that planning ahead will help me to make a rational decision because I will have looked at all of my options as well as opportunities in the fi

?Children mimic what their parents do and say but the developmental process differs for each child. Each child learns at his or her own pace, including when they learn to talk. A child begins to speaking process by forming basic sounds. Their first sounds are cooing and crying. Crying helps an infant's vocal cords and jaws develop for speaking. Infants hear sounds called phonemes, but they also begin to recognize the vibrations of their parents voices by six months old. The basic sound of their native language is understood, and typically, a child's first word is a simple noun. Controlled and repetitive sounds allow children to create syllables. By 18 months, children will be speaking several words but not in a particular order. However, their words will be synonymous with their wants; for instance, they may want more milk. Children may point at the things they want instead of saying the actual words. The parents say the words. Upon hearing the words being said, children will re

Golazo is a local Seattle company that started in October 2010 by co-founders Richard Tait and Alex Rosnast in order to provide energy and sports drink goods. The name Golazo came from the Spanish word meaning a brilliant goal in soccer (Golazo, 2010). Often, passionate soccer fans scream this word to celebrate their favorite team's goal. The vision of the co-founders is "we are the passion brand for soccer. With the ball as our compass we will create a platform for human potential and the belief that everyone is born to score!" (Golazo, 2010) With that, Golazo offers energy drinks and sports hydration drinks that have all natural ingredients with Latin-inspired flavors that target people who are passionate for the sport and enjoy Latin culture. The company operates mostly in the Seattle area, but has recently expanded its products to the Southern California region. Unfortunately, Golazo has no global strategies because of the company's young age. In order to share

"When major negative life events occur, or more serious or prolonged problems arise, coping becomes progressively more difficult." (Mental Health Continuum) After many sessions with Holden I was able to determine his physical and mental health. At initial patient profile it was determined that Mr. Caulfield is a 17-year-old boy who goes to Pency Prep Boarding School. He has failed out of many schools and doesn't seem to care about much of anything. As I noticed, many of Mr. Caulfield's problems are caused by his inability to grow up, come to terms with death, not be jealous, find his identity, and learn to interact in a social setting. He learns many lessons the hard way, and he is especially shaped through the experiences of a few days of freedom. Holden has shown signs of improvement after initial patient profile. Mr. Caulfield has continued to evolve his outlook on society. He has taken more of a positive stance on his own life. Holden discussed his feelings

New parents in the U.S. are guaranteed their jobs for 12 weeks after the arrival of a new baby. The law requires larger employers and public agencies to provide up to 12 weeks of unpaid leave, a continuation of health benefits for the birth or adoption of a child, or to care for an opposite-sex spouse, a parent or a child who has fallen ill. The law only requires companies with 50 or more employees to comply to get the benefits and employees must also have worked for the company for at least a year and logged 1,250 hours within the last 12 months. However some employees do not have to be paid during that time and are not offered the same benefits if they are part of a small company. How do US policies compare with those of 2 other countries? As stated in the New York Times article "In Paid Family Leave, U.S. Trails Most of the Globe", most of Europe and Central Asia provide 26 weeks or more of paid leave for mothers. In Switzerland, women are allowed 14 weeks of maternity leave and

International relations political theorist arguments can be found in both the newspaper articles "Olympic Arrogance" in The New York Times by Jules Boykoff and Alan Tomlinson and "Are Olympic Missiles Just for Show?" in BBC News UK by Stephen Dowlin, and as well as in the film made by Get Set To Go for Truce, produced for the London 2012 Olympics. Jules Boykoff and Alan Tomlinson take a Critical paradigm view of certain aspects of the Olympic games as they focus on how the International Olympic Committee came to be and who is it serving; Stephen Dowling in the other hand focuses on the necessity of the anti-aircraft missiles, part of the security measures for the Games; and the video shows the positive impact of what can happen when countries agree to work together through the Olympic Truce. The topic each deals with, combined with the way their facts and arguments were sustained make the 3 arguments very persuasive. Jules Boykoff and Alan Tomlinson criticize the

Did you know that the average American goes out to eat four to five times a week? Many of us have made stopping to get a burger or stopping at a fast food restaurant a part of our daily routine. Fast food is typically inexpensive, served quickly and requires no clean up at the end of a busy work day. And, above all, most fast food is delicious! Even though fast food is inexpensive, convenient and tasty, it is far from a healthy alternative to a home-cooked meal built on the four basic food groups. People who eat a lot of fast food should be very concerned about their health. It's easy to forget (or overlook) how unhealthy fast foods is but it would be prudent to remember that eating healthy foods not o

?******* ******** ****** ***********@gmail.com 858.555.5555 5555 Electric Ave. #1 San Diego, CA 55555 Educator Experienced Head Camp Counselor BA Degree in Spanish/Chicano Studies...Certificated Teacher Proven leadership skills as Head Camp Counselor for approximately 200 campers. Track record of interacting effectively with youth, parents, families and other staff. Particularly skilled at consensus building and negotiating resolution of complex issues. Bachelor of Arts from Claremont McKenna College with a dual major in Spanish and Chicano Studies. Fluent in English and Spanish Experienced leader and c