Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - Chapter Review Exercises - Page 591: 18



Work Step by Step

\begin{align*} \lim _{n \rightarrow \infty} c_{n}&=\lim _{n \rightarrow \infty} \sqrt{n^{2}+n}-\sqrt{n^{2}-n} \frac{\sqrt{n^{2}+n}+\sqrt{n^{2}-n}}{\sqrt{n^{2}+n}+\sqrt{n^{2}-n}}\\ &= \lim _{n \rightarrow \infty} \frac{2 n}{\sqrt{n^{2}+n}+\sqrt{n^{2}-n}}\\ &=\lim _{n \rightarrow \infty} \frac{2 }{\sqrt{1+1/n}+\sqrt{1-1/n}}\\ &=1 \end{align*}
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