$\text {The series } \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } n } { 6 n + 4 } \text { converges. }$

Name: $\text {The series } \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } n } { 6 n + 4 } \text { converges. }$
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Question

Quizplus · Accepted Answer

The series does not converge because the terms $\frac{n}{6n+4}$ do not approach zero as $n$ approaches infinity, which is a necessary condition for convergence of an alternating series.

The series ∑n=1∞(−1)n+1n6n+4 converges. \text {The series } \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } n } { 6 n + 4 } \text { converges. }The series ∑n=1∞​6n+4(−1)n+1n​ converges.

$\text {The series } \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } n } { 6 n + 4 } \text { converges. }$