Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 547: 3


$$\frac{5}{4},\quad \frac{205}{144}, \quad \frac{5369}{3600}.$$

Work Step by Step

We have $$ S_{2}=1+\frac{1}{2^2}=1+\frac{1}{4}=\frac{5}{4},\\ S_{4}=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}\\ =1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}=\frac{205}{144},\\ S_{6}=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}\\ =1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}=\frac{5369}{3600} $$
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