Provide an appropriate response.
-For an alternating series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } u _ { n }$ where it is not true that $u _ { n } \geq u _ { n } + 1$ for sufficiently large $n$, what can be said about the convergence or divergence of the series?
A) The series always diverges.
B) The series always converges.
C) The series may or may not converge.

Question

Quizplus · Accepted Answer

The Alternating Series Test states that if the series is alternating, decreasing in absolute value, and the limit of the absolute value of the terms is 0, then the series converges. Since we don't know if the terms are decreasing, we can't say for sure if the series converges or diverges. Therefore, the series may or may not converge.

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