CPM Homework Help : CALC Problem 10-150

Find the radius and interval of convergence for each of the following power series.

$\displaystyle\sum _ { k = 1 } ^ { \infty } \frac { ( - 4 ) ^ { k } ( x - 3 ) ^ { k } } { k }$
$\displaystyle\sum _ { k = 1 } ^ { \infty } \frac { 2 ^ { k } ( x + 4 ) ^ { k } } { ( k + 1 ) ! }$
$1 + 3 x + \frac { 9 x ^ { 2 } } { 2 } + \frac { 27 x ^ { 3 } } { 3 } + \frac { 81 x ^ { 4 } } { 4 } +$
$\displaystyle\sum _ { k = 2 } ^ { \infty } \frac { x ^ { k } } { 3 ^ { k \operatorname { ln } ( k ) } }$

Step (c):

$=\sum_{k=0}^\infty \frac{(3x)^k}{k}$

Partial answer (d):

After applying the Ratio Test, you should get:

$3|x|<1$

Now test the convergence of the series using the endpoints of the interval.