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If the sum of the series sum(n=0)^oor^n ...

If the sum of the series `sum_(n=0)^oor^n ,|r|<1` is `s ,` then find the sum of the series `sum_(n=0)^oor^(2n)` .

Text Solution

Verified by Experts

The correct Answer is:
`s^2/(2s-1)`
`s=sum_(n=0)^(oo)r^(n)=1+r+r^(2)+r^(3)+…`to `oo=1/(1-r)`
`rArrr=1-1/s=(s-1)/s`
`rArr sum_(n=0)^(oo)r^(2n)=1/(1-r^(2))=1/(1-((s-1)^(2))/s^(2))=s^(2)/(2s-1)`
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