CPM Homework Help : CALC Problem 10-43

Examine the following series. Use one of the tests you have learned so far to determine if the series converges or diverges. Name the test that you used.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \operatorname { ln } n }$
Hint (a):
This is an alternating series.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 5 } { n }$
Hint (b):
This is a form of the harmonic series.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { \pi } }$
Hint (c):
$π$ is just a number, so this is a $p$ -Series.

$\displaystyle\sum _ { n = 1 } ^ { \infty } 2 ( \frac { 5 } { 4 } ) ^ { n }$
Hint (d):
This is a geometric series. What is the value of $r$ ?