Let . Consider the two series and Determine all values of for which the sum of series…

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

0<t<1

. Consider the two series

A = \displaystyle \sum_{n=0}^{\infty} t^{n}

and

B = \displaystyle \sum_{n=0}^{\infty} \left(0.5\right)^{n}.

Determine all values of

t

for which the sum of series

A

is greater than the sum of series

B