Given that , determine the sum of the series followed by the remaining terms written…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Given that

\sum_{n=1}^{\infty}\dfrac{1}{2^{n}}=1

, determine the sum of the series

\tfrac1{2^{10}}+\tfrac1{2^{9}}+\cdots+\tfrac1{2^{1}}

followed by the remaining terms written in the same decreasing-exponent order. Justify your numerical answer.