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The value of sum(n=1)^oo(-1)^(n+1)(n/(5...

The value of `sum_(n=1)^oo(-1)^(n+1)(n/(5^n))` equals

A

`(5)/(12)`

B

`(5)/(24)`

C

`(5)/(36)`

D

`(5)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` We have `S=(1)/(5)-(2)/(5^(2))+(3)/(5^(3))-(4)/(5^(4))+(5)/(5^(5))+...oo`
`(S)/(5)=(1)/(5^(2))-(2)/(5^(3))+(3)/(5^(4))-(4)/(5^(5))+...oo`
Adding
`(6S)/(5)=(1)/(5)-(1)/(5^(2))+(1)/(5^(3))-(1)/(5^(4))-(1)/(5^(5))-...oo`
`(6S)/(5)=((1)/(5))/(1+(1)/(5))=((1)/(5))((5)/(6))impliesS=(5)/(36)`
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