Question

A. the series is absolutely convergent.

Answer 1

$\displaystyle\sum_{n=1}^\infty\left(1+\frac5n\right)^n$

Notice that

$\displaystyle\lim_{n\to\infty}\left(1+\frac5n\right)^n=e^5\neq0$

which means the series is divergent. So if this is one of those "select all that apply" questions, then both (c) and (j) are the only choices that do.