Mathematics

Mathematics

Problem

Define bn=e1/n−11/nb_n = \dfrac{e^{1/n}-1}{1/n} and consider ∑n=1∞bn\displaystyle\sum_{n=1}^{\infty} b_n. Which of the following is true? a) The series converges because lim⁡n→∞bn=0\displaystyle\lim_{n\to\infty} b_n = 0. b) The series diverges because lim⁡n→∞bn=1\displaystyle\lim_{n\to\infty} b_n = 1. c) The series converges because bn∼1/n2b_n \sim 1/n^{2} for large nn, a pp-series with p>1p>1. d) The series converges because lim⁡n→∞bn=1\displaystyle\lim_{n\to\infty} b_n = 1.

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