Classify each sequence as conditionally convergent, absolutelyconvergent, or

Chapter 9, Problem 3

(choose chapter or problem)

Classify each sequence as conditionally convergent, absolutely convergent, or divergent.

(a) $\sum_{k=1}^{\infty}(-1)^{k+1} \frac{1}{k}$ : ________.

(b) $\sum_{k=1}^{\infty}(-1)^{k} \frac{3 k-1}{9 k+15}$ : ________.

(d) $\sum_{k=1}^{\infty}(-1)^{k+1} \frac{1}{\sqrt[4]{k}^{3}}$ : ________.

Equation Transcription:

$\sum\limits_{k=1}^{\infty{}}$ $(-1{)}^{k+1}\frac{1}{k}$ :_____

$\sum\limits_{k=1}^{\infty{}}$ $(-1{)}^{k}\frac{3k-1}{9k+15}$ :_____

$\sum\limits_{k=1}^{\infty{}}$ $(-1{)}^{k}\frac{1}{k(k+2)}$ :_____

$\sum\limits_{k=1}^{\infty{}}$ $(-1{)}^{k+1}\frac{1}{\sqrt[4]{{k}^{3}}}$ :_____

Text Transcription:

Sum over k=1 ^infty (-1)^k+1 1/k:_____

Sum over k=1 ^infty (-1)^k 3k-1/9k+15:_____

Sum over k=1 ^infty (-1)^k 1/k(k+2):_____

Sum over k=1 ^infty (-1)^k+1 1/sqrt ^4_k^3:_____

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