CPM Homework Help : APCALC Problem 11-20

Consider the infinite series below. For each series, decide if it diverges, converges conditionally, or converges absolutely and justify your conclusion. State the tests you used.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { - 1 } { n + 2 }$
Hint (a):
This is a variation of the harmonic series.

$\displaystyle\sum _ { n = 1 } ^ { \infty } \operatorname { ln } ( n )$
Hint (b):
$\text{What is }\lim \limits_{n\to\infty}\ln(n)?$

$\displaystyle\sum _ { n = 1 } ^ { \infty } 0.1$
Hint (c):
$\text{What is }\lim \limits_{n\to\infty}0.1?$

$\displaystyle\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 1.01 } }$
Hint (d):
This is a $p$ -series.