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# Real Analysis : Radius and Interval of Convergence - Power Series (3 Problems)

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Determine the radius of convergence and the exact interval of convergence of the following power series...

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Solution.

(a) For
We know that if a power series converges, then it converges absolutely. So, we consider . We have the ratio of the n+1 term and the n-th term is

If , then converges. So,
converges. So, we know that the radius of the convergence is .

Now we consider ...

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