Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.2 Sequences - 8.2 Exercises: 18

Answer

$\lim\limits_{n \to \infty} n^\frac{2}{n}= 1$

Work Step by Step

To find the limit, we can evaluate $n^{\frac{2}{n}}$ for increasing values of $n$ and see what value it approaches. $1^\frac{2}{1} = 1$ $10^\frac{2}{10} = 1.585$ $100^\frac{2}{100} = 1.096$ $1000^\frac{2}{1000} = 1.012$ $10000^\frac{2}{10000} = 1.002$ As $n$ increases, the value of the terms seem to approach $1$.
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