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