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2nd - (ln n 4 n 2 b ∞ X n =1 2 n n n n c ∞ X n =1-1 n-1...

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MATH 120 RECITATION QUESTIONS WEEK 2 1. Use the integral test to show that X n =0 e - n 2 converges. 2. Show that X n =2 1 n (ln n ) p converges if and only if p > 1. 3. Does the series X n =2 ln n n 3 2 converge? 4. Determine whether X n =1 ( 1 n - sin 1 n ) converges or diverges. 5. For any positive number p show that the series X n =2 ( - 1) n ln n n p converges. Hint: Show that f ( x ) = ln x x p is decresing on [ e 1 p , ) so that if N is a positive integer greater than e 1 p then f ( n + 1) < f ( n ) for n > N . 6. Determine whether the following series converge or diverge. a )
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Unformatted text preview: (ln n ) 4 n 2 b ) ∞ X n =1 2 n n ! n n c ) ∞ X n =1 (-1) n-1 n 2 n + 1 7. Let a n = ± n 2 n , n odd 1 2 n , n even .Does ∞ X n =1 a n converge? 8. Which of the following series converge absolutely, which converge conditionally, and which diverge? a ) ∞ X n =2 cos( nπ ) n ln n b ) ∞ X n =1 cos( nπ ) n √ n c ) ∞ X n =1 (-1) n (2 n )! 2 n ( n !) n d ) ∞ X n =1 (-1) n ( √ n + 1-√ n ) 1...
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