THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer. a
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Pre-trip Background Research 1. History and heritage ** A nation’s dream of unity and common purpose now capable of realization 1.1 The earliest people - The earliest representatives of South Africa’s diversity – at least the earliest we can name – were the San and Khoekhoe peoples - Both were resident in the southern tip of the continent for thousands of years - The hunter-gatherer San ranged widely over the area - The pastoral Khoekhoe lived in those comparatively well-watered
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Introduction The current method of cell expansion using T25 flasks for human embryonic stem cells (hESCs) have been proven to be extremely time and space consuming‚ labour intensive and difficult for scale-up (Minimal of 200 T25 flasks needed). It is estimated 2.8x108 - 5.6x108 undifferentiated hESCs are required by the end of the expansion stage for the process to work‚ as at least 5x107 cells of well differentiated post-mitotic Nrl+/Crx+ precursors are needed for transplant (Maclaren et al‚ 2006)
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the War in Korea‚ the main intention was to gain South Koreas territory and to stop the spread of Communism. The war never really ended even while the Peace negotiations were currently happening. (Wikipedia) The war didn’t end till South Korea gained back its territory. South Korea built it’s heavily armed border between their side of the country and the North Koreans. The U.S. troops didn’t withdrawal from their occupation in South Korea since the main intention’s to stop the communist
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Natasha Black Assignment 1 Settlement West There are many reasons the settlers were motivated to face dangers and hardships to move west. They believed they would have better opportunities in the west that they did in the east. The west was completely open and a place for new beginnings. Farmland was available and no one owned anything so everything was available for them to take‚ many settlers made a living working on farms‚ so this brought on many job opportunities for them. The United
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How free really were African-Americans in the North? In the North African-Americans were free but treated as if they weren’t. They didn’t have as good a life as whites. Leading up to and during the civil war‚ blacks were either slaves or unequal free men. In the South they were most likely slaves and in the North they were free but they only had certain rights instead of all they should have. While African-Americans in the North were legally free‚ they were not equal because of social‚ political
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reasons why the North and South fought the Civil War. You turn on the computer and type out the following: The North and South fought the Civil War for many reasons‚ some of which were the same and some different. This weak thesis restates the question without providing any additional information. You will expand on this new information in the body of the essay‚ but it is important that the reader know where you are heading. A reader of this weak thesis might think‚ "What reasons? How are they the
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The North took victory in the civil war against the South. The North had several of advantages when it came to defeating the other side.The blockade. As the war progressed the blockade of Southern ports slowly became more effective‚ closing the ports and thus cutting off the vital supplies needed to fight the war. This includes medicine. The South had to rely on Europe even more so than the North for supplies with which to fight the war so by eliminating more and more ports into which the supplies
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The Bible’s Influence on Western Music Abstract: The Voice‚ one of the America’s most-watched TV shows‚ exhibits distinctly different styles of music by different color.‚ including American country music‚ Latin music‚ R&B‚ Jazz‚ Gospel music‚ etc. However‚ it’s tough to distinguish which style a certain song belongs to. It arouses my interest to find out what impacted western music during its long-term development and what the western music derived from. This article provides brief introductions
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client is open and understood. There are many different methods that can be used by the interpreter to ensure they do an outstanding job in relaying both messages to each party in need of an interpreter. One way to ensure this is expansion. There are several expansion techniques used by an interpreter to convey the meaning of the hearing person such as; contrasting‚ faceting‚ reiteration‚ explaining by example‚ using 3-D space‚ scaffolding and describe‚ then do. Contrasting technique is used
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