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Determine the radius of convergence and interval of convergence for the power series: ∞∑n=0 (x−7)n+1/nn.

Determine the radius of convergence and interval of convergence for the power series: ∞∑n=0 (x−7)n+1/nn. Correct Answer ∞, −∞<x<∞

So, L=limn→∞∣(x−7)n+1/nn∣ L=limn→∞∣x−7/n∣ L=|x−7|limn→∞1/n=0 So, since L=0<1 any of the value of x, this power series will converge for every x. In these cases, the radius of convergence is R=∞ and interval of convergence is −∞

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