## Thomas' Calculus 13th Edition

Published by Pearson

# Chapter 10: Infinite Sequences and Series - Practice Exercises - Page 636: 4

#### Answer

converges to $1$.

#### Work Step by Step

As we know that a sequence converges when $\lim\limits_{n \to \infty}a_n$ exists. Consider $a_n=1+(0.9)^n$ Apply limits to both sides. $\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}[1+(0.9)^n]$ $\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}(1)+\lim\limits_{n \to \infty}(0.9)^n$ $\lim\limits_{n \to \infty}a_n=1+0$ $\lim\limits_{n \to \infty}a_n=1$ Therefore, the sequence converges to $1$.

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