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: 27


$S_4\approx −0.183333$ $S_7 \approx 0.065079 $

Work Step by Step

Given $$\sum_{n=1}^{\infty} \frac{n-2}{n^{2}+2 n}$$ Since \begin{align*} S_4 &= \sum_{n=1}^{4} \frac{n-2}{n^{2}+2 n}\\ &= \frac{-1}{3}+0+\frac{1}{15} +\frac{2}{24}\\ &\approx −0.183333 \end{align*} and \begin{align*} S_7 &= \sum_{n=1}^{7} \frac{n-2}{n^{2}+2 n}\\ &= \frac{-1}{3}+0+\frac{1}{15} +\frac{2}{24} + \frac{3}{35}+\frac{4}{48}+\frac{5}{63}\\&\approx0.065079 \end{align*}
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