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: 32



Work Step by Step

The series $\sum_{n=2}^{\infty}\left(\frac{2}{e}\right)^{n}$ can be rewritten as follows $$ \sum_{n=2}^{\infty}\left(\frac{2}{e}\right)^{n}= \left(\frac{2}{e}\right)^{2}+\left(\frac{2}{e}\right)^{3}+\cdots \\ =\sum_{n=0}^{\infty}\frac{4}{e^2}\left(\frac{2}{e}\right)^{n}. $$ Now, we have a geometric series which has the sum $$\frac{c}{1-r}=\frac{4/e^2}{1-(2/e)}=\frac{4}{e^2-2e}.$$
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