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  • Find the sum of the terms of the series $1, \frac{4}{5}, \frac{16}{25}, \frac{64}{125}, \ldots \ldots \ldots \infty$Option: 1 25<

Find the sum of the terms of the series

$1, \frac{4}{5}, \frac{16}{25}, \frac{64}{125}, \ldots \ldots \ldots \infty$

Option: 1

25


Option: 2

135


Option: 3

5


Option: 4

125


Answers (1)

It can be noticed that the given series is a G.P. with infinite terms. The common ratio is (4/5) and this is < 1.

The sum to infinity of a series with first term a and the common ratio

$r=[a /(1-r)]$

As $a=1$ and $r=4 / 5$

the sum to infinity $=\frac{1}{1-(4 / 5)}=5$

Posted by

Kshitij

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