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The sum of the series (9)/(5^(2)*2*1)+(1...

The sum of the series `(9)/(5^(2)*2*1)+(13)/(5^(3)*3*2)+(17)/(5^(4)*4*3)+...` upto infinity

A

`1`

B

`(9)/(5)`

C

`(1)/(5)`

D

`(2)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `T_(r )=(4r+1)/(5^(r )r(r-1))`, `r ge 2`
`=(5r-(r-1))/(5^(r)r(r-1))`
`=(1)/(5^(r-1)(r-1))-(1)/(5^(r)r)`
`:.sum_(r=2)^(oo)T_(r )=(((1)/(5^(1)*1)-(1)/(5^(2)*2))+((1)/(5^(2)*2)-(1)/(5^(3)*3))+((1)/(5^(3)*3)-(1)/(5^(4)*4))+...oo)`
`(1)/(5)`
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