Solution: Apply integral test: Z Z ln R 1 X R 2 1 p dx x (ln x) p=1 p 6= 1 let ln (x) = u then ln 2 so that when p = 1 and p < 1 integral diverges by letting R ! 1‚ so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln 2) lim = ‚ R!1 1 p 1 p 1 p so does the series. 2. (18 pts.) Find the in…nite sum 1 : n (n + 2) n=1 Solution: See that 1 1 = n (n + 2) n 1 n+2 1 X 8 R < ln ujln 2 ln 1 ln R du = 1 p : u p up 1 ln 2 hence 1 n (n + 2) n=1 k X
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Atheism "Atheist" redirects here. For other uses‚ see Atheist (disambiguation). Part of a series on Atheism Concepts Antitheism Atheism and religion Criticism of atheism Implicit and explicit atheism Negative and positive atheism History History of atheism New Atheism State atheism Arguments for atheism Arguments against God’s existence Argument from free will Argument from inconsistent revelations Argument from nonbelief Argument from poor design Atheist’s Wager Fate of the unlearned
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WAR WAR. The very sound of those three letters can conjure up feelings and images of fighting‚ explosions‚ fear‚ sorrow‚ hate‚ and most importantly death‚ especially to those who have been in one or even two. But not everything associated with war is a bad thing. For some‚ war gives people hope‚ faith‚ understanding‚ and camaraderie‚ amongst other things. There are many reasons why a war starts. It could be a civil war‚ in which a whole singular country fights within itself or even
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waging war and breaking away from Britain during the Revolutionary War? The colonists were justified in waging war and breaking away from Britain during the revolutionary war. The war for American independence began with in 1775 and lasted at least until 1783 when the peace treaty with the British was signed. The colonies of England wanted to be independent and no longer serve the mother country. After the French and Indian war in 1754-1763 Britain nor the colonies wanted to pay for the war‚ both
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Chapter One: A New World The most detailed American historical records begin after European colonization (2). Countless amounts of people recorded the history America captivated until the present times. Answers to many of the questions some people have about America hides in the past‚ but a good amount of documents provide the public important evidence for some. Explaining how Europeans settled in the New World with various ways of doing so‚ and why Indians and Europeans live differently will take
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There were many challenges for Americans in the 1930’s to the mid 1940’s. Most notably‚ a decade of depression and the confrontation of war; the deadliest war in history. When World War II ended in September of 1945‚ America emerged as the most powerful nation in the world. American society transformed; the population shifted to the suburbs‚ the G.I. Bill was created to benefit (most) WWII veterans‚ and consumerism played many effects on society. By 1920‚ over fifty-four million American’s were
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African Americans had been mistreated many years before the Civil War in the United States‚ and around the world. When the Civil War ended they thought they would have as many rights as whites‚ but they were wrong. This mistreatment‚ segregation‚ and racism continued well past the turn of the century‚ and even beyond World War I. Nowadays African American soldiers‚ and citizens of the world alike have so many more opportunities than back in the late 1800s and early 1900s. As Addie W. Hunton‚ Kathryn
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| Wal-Mart expansion in France | Management of International Business | | Gemma Barlow 33246023 | Mahfuz Rahman | 12/17/2012 | | Plagiarism Declaration I certify by my signature/printed name that this is my own work. The work has not‚ in whole or in part‚ been presented elsewhere for assessment. Where material has been used from other sources it has been properly acknowledged and referenced. If this statement is untrue I acknowledge that I will have committed an assessment
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Kiara Milho Reconstruction DBQ December 27‚ 2013 From the start of the American Civil War until the end of Reconstruction‚ the United States of America suffered what can be considered a revolution. During this time many constitutional and social developments brought about a great change in the country. Some constitutional developments that caused conflict were the Emancipation Proclamation‚ three civil rights bills‚ and the reconstruction‚ while some social developments which could potentially
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France and 1871 • France declared war on Prussia on 10th of July in 1870 following “Ems Dispatch “after declaration of the status of the second French empire ➢ Otto von Bismarck manipulated the telegram by Wilhelm 1 that is sent to France and published to the public. ➢ In respect of France‚ the manipulated telegram sound as if the king mistreated them. ➢ 6 days later‚ France declared war of Prussia. • Then from August to September‚ French forces had lost continuously
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