Question

In the following problems, determine if the series converges. If it does, is the convergence conditional or absolute?

1) \[\sum_{n=1}^{\infty} e ^{1/n}/n ^{2} \]
a)using alternating test
b)using integral test

2) \[\sum_{n=1}^{\infty} (−1)n \cos(\pi n) \]

3) \[\sum_{n=1}^{\infty} (-1)^{n}/n!\]

4) \[\sum_{n=1}^{\infty}2^{n}n!/n ^{n} \]

Answer 1

1) \[\sum_{n=1}^{\infty} e ^{1/n}/n ^{2} \]
a) using alternating test
b) using integral test 2) \[\sum_{n=1}^{\infty} (−1)n \cos(\pi n) \] 3) \[\sum_{n=1}^{\infty} (-1)^{n}/n!\]
4) \[\sum_{n=1}^{\infty}2^{n}n!/n ^{n} \]