MATH 141E Series Practice 1

MATH 141E Series Practice 1 - SERIES PRACTICE Does each...

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Unformatted text preview: SERIES PRACTICE Does each series converge or diverge? What test would you use to show this? Find the sum of the series when easily possible with our current methods. 1) ∞ ∑ n =1 1 n 1 . 1 2) ∞ ∑ n =2 1 n 2- 1 3) ∞ ∑ n =- 1 4 n +1 5 n 4) ∞ ∑ n =1 (- 1) n n √ n 2 + 1 5) ∞ ∑ n =1 (- 1) n n √ n 3 + 1 6) ∞ ∑ n =1 n √ n 3 + 1 7) ∞ ∑ n =1 5 + sin n n 8) ∞ ∑ n =2 1 n ln n 9) ∞ ∑ n =1 tan- 1 n n 4 10) ∞ ∑ n =2 n ( n- 1)2 n 11) ∞ ∑ n =1 n ln n ( n + 1) 4 12) ∞ ∑ n =2 (- 1) n +1 n 4 n- 1 13) ∞ ∑ n =1 ln parenleftBig n 3 n +1 parenrightBig 14) ∞ ∑ n =1 ln parenleftBig n n +1 parenrightBig 15) ∞ ∑ n =1 1 2 n + 3 16) ∞ ∑ n =1 n 2 5( n + 1)( n + 3) 17) ∞ ∑ n =2 (- 1) n +1 e 2 n 18) ∞ ∑ n =1 3 5 n- e n 19) ∞ ∑ n =2 1 ln(ln n ) 20) ∞ ∑ n =2 (- 1) n ln n n 3 / 2 21) ∞ ∑ n =2 ln n n 3 / 2 22) ∞ ∑ n =1 3 n 2- √ n √ 2 n 5- n + 8 23) ∞ ∑ n =1 1 + cos n 3 n 24) ∞ ∑ n =1 n n n !...
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This note was uploaded on 04/12/2008 for the course MATH 141E taught by Professor Spaeth during the Spring '08 term at Penn State.

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MATH 141E Series Practice 1 - SERIES PRACTICE Does each...

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