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Simkate

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∑ (4^n x^n)/([log(n+1)]^(n)

(a) the radius of convergence

(b) the interval of convergence, discussing the endpoint convergence when

the radius of convergence is finite.

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I wanted to know whether my solution is write, is it possible for somone to check it for me. Thank You

Due to the n-th powers, we use the root test.

r = lim(n-->∞) |4^n x^n / [log(n+1)]^n|^(1/n)

= lim(n-->∞) 4|x| / log(n+1)

= 0 for all x.

a) radius of convg= 0

b) interval of convg=0

since the series is infinte