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Find the sum of the series 1+4/5+7/(5^2)...

Find the sum of the series `1+4/5+7/(5^2)+10/(5^3)+...`

A

`7//16`

B

`5//16`

C

`105//64`

D

`35//16`

Text Solution

Verified by Experts

The correct Answer is:
D
Let
` S=1+4/5+7/5^(2)+10/5^(3)+..oo`
Then
`1/5S=1/5+4/5^(2)+7/5^(3)+..oo`
or `S(1-1/5)=1+3[1/5+1/5^(2)+1/5^(3)+..oo]`
or `4/5S=1+3xx(1//5)/(1-(1//5))=1+3/4=7/4`
or `S=35/16`
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