Provide an appropriate response.
-For an alternating series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } u _ { n }$ where $\lim _ { n \rightarrow u _ { n } } \neq 0$, what can be said about the convergence or divergence of the series?
A) The series may or may not converge.
B) The series always converges.
C) The series always diverges.

Question

Quizplus · Accepted Answer

For an alternating series to converge, one of the necessary conditions is that the limit of $u_n$ as $n$ approaches infinity must be 0. If $\lim _ { n \rightarrow \infty } u _ { n } \neq 0$, the series does not meet this condition and therefore must diverge.

Provide an Appropriate Response ∑n=1∞(−1)n+1un\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } u _ { n }∑n=1∞​(−1)n+1un​

Provide an Appropriate Response $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } u _ { n }$