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The sum of an infinite geometric series ...

The sum of an infinite geometric series is `15` and the sum of the squares of these terms is `45`. Find the series.

Text Solution

Verified by Experts

Given,

`S_(o o)=(a)/(1-r)=15`

Squaring both sides,

`(a^2)/((1-r)^2)=225``\ \ \ (1)`

Sum of square of terms in G.P.

`(a^2)/((1-r)(1+r))=45``\ \ \ (2)`

Dividing `(1)` by `(2)`

`(1+r)/(1-r)=5`

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