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 - Preliminary Questions - Page 546: 4


This is not valid reasoning.

Work Step by Step

This is not valid since the expanded series is: $$S_n=1+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\cdots+\frac{1}{2^n}$$ Clearly, the sum will not be zero. In other words, if the terms tend toward zero, this does not mean that they will sum to zero.
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