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sum(k=1)^ook(1-1/n)^(k-1)=>? a.n(n-1)...

`sum_(k=1)^ook(1-1/n)^(k-1)=>? a.`n(n-1)` b. `n(n+1)` c. `n^2` d. `(n+1)^2`

A

`n(n-1)`

B

`n(n+1)`

C

`n^(2)`

D

`(n+1)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(k=1)overset(oo)sumk(1-1/n)^(k=1)`
`=1-2(1-(1)/(n))^(1)+3(1+1/n)^(2)+"….."`
`= 1+2r+3t^(2)+"…"`
`= (1-t)^(-2)`
`= [1-(1-(1)/(n))]^(-2) = (1/n)^(-2) = n^(2)`
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