University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.2 - Sigma Notation and Limits of Finite Sums - Exercises - Page 300: 41



Work Step by Step

Here, we have $f(x)=1+x^2$ Then, $\Sigma_{i=1}^n (\dfrac{3}{n}) (1+c_i)^2=(\dfrac{27}{n^3}) \Sigma_{i=1}^n (3+i^2)$ or, $3+(\dfrac{27n(n+1)(2n+1)}{6n^3})-(\dfrac{1}{n^3}) \Sigma_{i=1}^n i^2)=\dfrac{18+27/n+9/n^2}{2}+3$ Thus, $\Sigma_{i=1}^n (\dfrac{3}{n}) (1+c_i)^2=9+3=12$
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