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  4. The sum value of the infinite series 1+(1/5)+(1/25)+(1/125)+(1/625)+....∞ is

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Q. The sum value of the infinite series $ 1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\frac{1}{625}+....\infty $ is

J & K CETJ & K CET 2018

Solution:

The given series is,
$ 1 +\frac{1}{5} + \frac{1}{5^2} + \frac{1}{5^3} + .....\infty$
which is a $G.P.$ with first term $(a) = 1$
and common ratio $(r) = \frac{1}{5}$
$\therefore $ Sum of infinite terms $ = \frac{1}{1- \frac{1}{5}} = \frac{5}{4}$