Determine the convergence or divergence of the series $\sum _ { n = 1 } ^ { \infty } \frac { 7 ( - 1 ) ^ { n + 1 } } { n }$ using any appropriate test.
A) converges
B) diverges

Question

Determine the convergence or divergence of the series $\sum _ { n = 1 } ^ { \infty } \frac { 7 ( - 1 ) ^ { n + 1 } } { n }$ using any appropriate test. 
A) converges
B) diverges

Quizplus · Accepted Answer

This series is an example of an alternating series, which can be analyzed using the Alternating Series Test. The test states that an alternating series $\sum (-1)^n a_n$ converges if the sequence $a_n$ is decreasing and its limit as $n$ approaches infinity is 0. In this case, $a_n = \frac{7}{n}$, which is a decreasing sequence and its limit as $n$ approaches infinity is 0. Therefore, the series converges.

Determine the Convergence or Divergence of the Series ∑n=1∞7(−1)n+1n\sum _ { n = 1 } ^ { \infty } \frac { 7 ( - 1 ) ^ { n + 1 } } { n }∑n=1∞​n7(−1)n+1​

Determine the Convergence or Divergence of the Series $\sum _ { n = 1 } ^ { \infty } \frac { 7 ( - 1 ) ^ { n + 1 } } { n }$