1+ \frac{2}{3}+( \frac{2}{3})^{2}+( \frac{2}{3})^{3}+..... to infinity =

AP ICET 2015 Paper

Question : 74 of 200

Marks: +1, -0

1+\;\;{2}/{3}+(\;\;{2}/{3})^{2}+(\;\;{2}/{3})^{3}+.....

to infinity =

Solution:

Given :

1+{2}/{3}+({2}/{3})^{2}+({2}/{3})^{3}+.....

to infinity
The given infinite series is a G.P.
First term, a = 1, common ratio,

r =2/3 < 1

sum

S_∞=a/{1-r}=1/{1-2/3}=3

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