1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\frac{1}{625}+......\infty=

AP ICET 2016 Paper

Question : 67 of 200

Marks: +1, -0

1+{1}/{5}+{1}/{25}+{1}/{125}+{1}/{625}+......∞=

Solution:

Given :

1+{1}/{5}+{1}/{25}+{1}/{125}+{1}/{625}+.....

=1+1/5+1/5^2+1/5^3+....

It is an infinite G.P.
First term, a = 1
Common ratio,

r=1/5

S_{∞}={a}/{1-r}={1}/{(1-{1}/{5})}={5}/{4}

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