Calculus (3rd Edition)

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

Chapter 5 - The Integral - 5.1 Approximating and Computing Area - Exercises - Page 235: 26


$$\sum_{i=1}^{n} \sqrt{i+i^{3}}$$

Work Step by Step

Given $$\sqrt{1+1^{3}}+\sqrt{2+2^{3}}+\dots+\sqrt{n+n^{3}}$$ The first term is $ \sqrt{1+1^{3}}$, the last term is $\sqrt{n+n^{3}}$, and we observe that terms are increasing by $1$, so $$\sqrt{1+1^{3}}+\sqrt{2+2^{3}}+\dots+\sqrt{n+n^{3}}=\sum_{i=1}^{n} \sqrt{i+i^{3}}$$
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