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

question 135

Multiple Choice

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.