CPM Homework Help : APCALC Problem 10-87

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

$\displaystyle\sum _ { n = 1 } ^ { \infty } ( 2 ^ { - n } + 3 ^ { - n } )$
Hint (a):
This is the sum of two geometric series. Do both of these series converge?

$\displaystyle\sum _ { n = 1 } ^ { \infty } e ^ { - n }$
Hint (b):
This is a geometric series. What is the value of $r$ ?

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { \operatorname { ln } ( n ) } { n ^ { 2 } }$
Hint (c):
$\sqrt{n}>\ln(n)$
More Help (c):
$\frac{\sqrt{n}}{n^2}=\frac{1}{n^{1.5}}>\frac{\ln(n)}{n^2}$