Calculus (3rd Edition)

Published by W. H. Freeman

Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 538: 46

Answer

$0$

Work Step by Step

We have $$\lim_{n\to \infty}c_n=\lim_{n\to \infty}\frac{(-1)^n}{{\sqrt n}}.$$ Since $-1\leq (-1)^n \leq 1$, then $-\frac{1}{\sqrt{n}}\leq \frac{(-1)^n}{\sqrt{n}}\leq \frac{1}{\sqrt{n}}$. Applying the squeeze rule, we find that $$\lim_{n\to \infty}\frac{(-1)^n}{{\sqrt n}}=0.$$ Hence, by Theorem 1 the sequence $c_n$ converges to $0$.

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