Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 825: 82


Geometric Sum: $0$

Work Step by Step

We are given the sequence: $\{(-1)^n\}$ Compute the ratio between two consecutive terms: $\dfrac{a_{k+1}}{a_k}=\dfrac{(-1)^{k+1}}{(-1)^k}=-1$ As the ratio between any consecutive terms is constant, the sequence is geometric. Its elements are: $a_1=(-1)^1=-1$ $r=-1$ We determine the sum of the first 50 terms: $S_n=a_1\cdot\dfrac{1-r^n}{1-r}$ $S_{50}=(-1)\cdot\dfrac{1-\left(-1\right)^{50}}{1-(-1)}=0$
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