Find the radius of convergence and the interval of convergence
of the series.
- (a) (6 points)

- (b) (6 points)

When we do, the interval will be

. However, the boundary values for

,

and

must be tested individually for convergence. Many times, one boundary value will produce an alternating, convergent series while the other will produce a divergent, non-alternating series. As a result, intervals of convergence may not be strictly open.
Foundations:
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When we are asked to find the radius of convergence, we are given a series where
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where and are functions of and respectively, and is a constant (frequently zero). We need to find a bound (radius) on such that whenever , the ratio test
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Solution:
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