Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 580: 61

Answer

Diverges

Work Step by Step

Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Consider the series $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{1000^n}$ . Here, the numerator terms will be increased more than the terms on denominator. Also, $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{1000^n}=\infty \ne 0$ Hence, the series diverges.
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