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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Democrat and Republican Parties of the late 1800’s Essay The Democrat and Republican parties of the late 1800’s had a parallel belief that it was giving a voice to its constituents. The Republicans and Democrats fought over political corruption‚ civil rights‚ reconstruction‚ immigration‚ and States’ rights. Republicans appealed to the Union‚ Border States‚ and African Americans. The South had to be rebuilt‚ but giving power to the Southern whites was not an option at any time. Lincoln’s
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In 1860 and 1861 eleven of the southern states declared their secession from the Union creating the Confederate States. This act caused widespread conflict and the Civil War followed quickly after. The Southern states were led to secede from the Union by many different factors‚ including the question of slavery‚ the election of Abraham Lincoln‚ and the “right of self government.” In 1850‚ John C. Calhoun asked the question‚ “What is it that has endangered the Union?” in his speech "The Clay Compromise
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COLONIAL EXPANSIONS AND RIVALRIES What is it? Colonialism expansion is where countries (such as Britain‚ France‚ Germany and Russia) settle on new land. They do this to expand their territories‚ and to use their resources for to benefit their empire. Rivalries between the empires are consequential. This is because many empires are involved in conflicts when attempting to regain new land. How did it contribute to the start of World War I? Imperialism was one of the causes of World War I.
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Economic Expansion 1. Briefly describe Hong Kong’s economy (background‚ GDP‚ growth rate‚ etc.)‚ (20 points) Everything about Hong Kong tells the story of trade. With beginnings as a small rocky island full of fishing villages‚ Hong Kong has grown to become one of the largest cities of trade and finance in the world. Hong Kong had a GDP of $325.8 billion USD in 2010‚ which represents a 6.8% growth from the previous year (“Economy: Hong Kong”‚ 2011). This growth is a nice change from the 2.7% loss
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Beginning in 1800s America began a mission of western expansion. Americans knew that they wanted to expand and grow. The Monroe Doctrine was a foreign policy that regarded domination in the America’s‚ issued in 1823. This policy said that future efforts by the European nations to colonize land and interfere on American soil will be viewed as an act of aggression. This would require U.S intervention. Many Historians felt that the Monroe Doctrine enabled Americans to move west because no other countries
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Manifest Destiny was the phrase used when it came to speaking about the belief of destined westward expansion of the United States. In the 1800’s the concept influenced American policy and enforced the hasty development of the country. Widely known by newspapers and posters‚ Manifest Destiny was promoted throughout the east. During this time Indians were forced away to make room for the expansion and many lost their lives along the way. In the mid-nineteenth century‚ white Protestant Americans viewed
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The period from 1450 to 1650 is often referred to as the “Age of Discovery‚” an era of advances in geographical knowledge and technology. It was also a time of European migration to other parts of the world. This Age of Expansion and European exploration from 1450 to 1525‚ greatly promoted by economical‚ technological‚ political‚ and religious factors‚ launched a major turning point in world history. The economy of late fifteenth century played an important role in European conquest. The Ottoman
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1. How did the introduction of factories in the 1800s change the lives of people in Britain? The introduction of factories in Britain had some positives and negatives changes‚ it made the production of cotton‚ cigarettes and all the other things easier and cheaper‚ but it begun the child labour and people had terrible conditions. It was an evolution of the technologies‚ but also destroyed the life of many people. 2. What were the key differences between working in the domestic system and working
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our time of day. Even when slavery was abolished in 1865‚ it has unfortunately not been concluded to an end. The relevance of slavery in the modern United States is still sincere and yet hasn’t vanished. Many people will think about slavery in the 1800’s when one perceives the phrase “Slavery in the United States”. This is the problem of our society‚ no one has cognitioned the thought of modern slavery and at the end of the day‚ it’s not helping anyone. Under slavery‚ victims go through a rough time
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