### Home > APCALC > Chapter 10 > Lesson 10.1.5 > Problem10-57

10-57.

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

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \operatorname { ln } ( n ) }$

This is an alternating series.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 5 } { n }$

This is a form of the harmonic series.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { \pi } }$

$π$ is just a number, so this is a $p$-Series.

1. $\displaystyle\sum _ { n = 1 } ^ { \infty } 2 ( \frac { 5 } { 4 } ) ^ { n }$

This is a geometric series. What is the value of $r$?