College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises: 70

Answer

$\sum_{k=2}^{100}\frac{(-1)^{k}}{k\ln k}$

Work Step by Step

We write the sum in sigma notation: (We notice that the denominator takes the form $n\ln n$ with $n$ being an integer, while the numerator alternates between $1$ and $-1$.) $\frac{\mathrm{l}}{2\ln 2}-\frac{\mathrm{l}}{3\ln 3}+\frac{\mathrm{l}}{4\ln 4}-\frac{\mathrm{l}}{5\ln 5}+\cdots+\frac{\mathrm{l}}{100\ln 100}=\sum_{k=2}^{100}\frac{(-1)^{k}}{k\ln k}$
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