CPM Homework Help : CALC Problem 12-50

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12-50.

Find the interval of convergence for each series.

$\displaystyle\sum _ { n = 0 } ^ { \infty } \frac { 1 } { ( 2 n ) ! } x ^ { 2 n }$
Hint (a):
Once the Ratio Test is first applied, your result should be:

$\displaystyle\sum _ { n = 2 } ^ { \infty } n ^ { 2 } ( x + 1 ) ^ { n }$
Hint (b):
Once the Ratio Test is applied and simplified, your result should be:
Once you solve for $x$ , be sure to check the endpoints.

$\displaystyle\sum _ { n = 1 } ^ { \infty } ( \frac { n } { 2 n - 5 } ) ^ { n } x ^ { n }$
Hint (c):
$\lim\limits_{n\to\infty}\bigg|\Big(\frac{(2n-5)(n+1)}{(2n-3)n}\Big)^n\Big(\frac{n+1}{2n-3}\Big)x\bigg|$
Once you solve for $x$ , be sure to check the endpoints.

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