CPM Homework Help : CALC Problem 11-20

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11-20.

Consider the infinite series below. For each, decide if it converges or diverges and justify your conclusion. State the test 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):
What is $\lim\limits_{n\to\infty}\ln(n)?$

$\displaystyle\sum _ { n = 1 } ^ { \infty } 0.1$
Hint (c):
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.

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