Question

A. the series is absolutely convergent.

b. the series converges, but not absolutely.
c. the series diverges.
d. the alternating series test shows the series converges.
e. the series is a p-series. f. the series is a geometric series. g. we can decide whether this series converges by comparison with a p series. h. we can decide whether this series converges by comparison with a geometric series. i. partial sums of the series telescope. j. the terms of the series do not have limit zero. a 1. \displaystyle \sum^\infty_{n=1} \left( 1 + \frac{5 }{n} \right)^n

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\\eq0`

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.