CPM Homework Help : CALC Problem 12-7

Use an appropriate test to determine if the following series converge or diverge. State the test you used.

$\displaystyle\sum _ { n = 1 } ^ { \infty } ( 1 - \frac { 3 } { n } ) ^ { 3 n }$

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

$\displaystyle\sum _ { k = 1 } ^ { \infty } \frac { \operatorname { ln } k } { k ^ { 3 } }$

$\displaystyle\sum _ { k = 5 } ^ { \infty } k ! e ^ { - k }$

Hint:

You should recognize the argument of the summation as representing a special value.
Which is dominant when $k > 5$ , the numerator or the denominator?