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

`sum_(k=1)^ook(1-1/n)^(k-1) ` =?

`n(n-1)`

`n(n+1)`

`n^(2)`

`(n+1)^(2)`

Text Solution

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The correct Answer is:

`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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