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Unformatted text preview: I n = Z 1 ( ln x ) n d x , n > (a) Find an equation relating I n and I n1 . (b) It can be shown that I n = (1 ) n n ! Determine whether the sequence { I n } n = 1 converges or diverges. Explain your reasoning. 5. ( 21 points, 7 each ) Determine whether the sequences below converge or diverge. You must explain your reasoning. (a) { ln nln ( n + 1 ) } n = 1 (b) sin n n n = 1 (c) { a n } n = 1 where for all n > 1, a 2 n = 0, a 2 n + 1 > a 2 n1 , a 1 = 1 and a n < 2. 6. ( 21 points, 7 each ) Determine whether the series below converge or diverge. You must explain your reasoning. ( a ) X n = 1 n n + 1 , ( b ) X n = 2 1 n ln ( n 2 ) , ( c ) X n = 1 sin 4 n 7. ( 6 points ) Calculate the innite sum: 0.4 + 0.16 + 0.064 + 0.0256 + . . . Good Luck!!!...
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 Winter '06
 LIM,JISUN

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