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: 27



Work Step by Step

Given $$\frac{1}{2 \cdot 3}+\frac{2}{3 \cdot 4}+\dots+\frac{n}{(n+1)(n+2)}$$ The first term is $\dfrac{1}{2 \cdot 3}=\dfrac{1}{(1+1)(1+2)}$, the last term is $\dfrac{n}{(n+1)(n+2)}$, and we observe than the numerator is increasing by $1$, so $$\frac{1}{2 \cdot 3}+\frac{2}{3 \cdot 4}+\dots+\frac{n}{(n+1)(n+2)}=\sum_{i=1}^{n}\frac{i}{(i+1)(i+2)}$$
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