Identify the interval of convergence of a power series .

Name: Identify the interval of convergence of a power series .
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Question

Identify the interval of convergence of a power series  .

Quizplus · Accepted Answer

By applying the ratio test, we get:

lim (n→∞) |(11/(n+1))^n / (11/n)^n| = lim (n→∞) |(n/(n+1))^n|
= lim (n→∞) |(1+1/n)^(-n)| = 1/e

Since the limit is finite and less than 1, the series converges by the ratio test. Therefore, the interval of convergence is (-∞, ∞), which is choice B.

Identify the Interval of Convergence of a Power Series