Question

Prove whether the series converges or diverges. n=2∑[infinity]​ (−1)n+16+n5+n​ The series is diverges

Answer 1

Diverges by A.S.T

Explanation:

`\displaystyle \sum^\infty_(n=2)(-1)^(n+1)(5+n)/(6+n)` is an alternating series, so to test its convergence, we need to use the Alternating Series test.

Since
`\displaystyle \lim_(n\rightarrow\infty)(5+n)/(6+n)=1\\eq0`, then the series is divergent.