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 - Page 601: 72



Work Step by Step

We write the sum in sigma notation: (We notice that the numerator takes the form $\sqrt{k}$, while the denominator takes the form $k^2$, with $k$ being consecutive integers.) $\frac{\sqrt{1}}{1^{2}}+\frac{\sqrt{2}}{2^{2}}+\frac{\sqrt{3}}{3^{2}}+\cdots+\frac{\sqrt{n}}{n^{2}}=\sum_{k=1}^{n}\frac{\sqrt{k}}{k^{2}}$
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