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If S is the sum to infinity of a G.P. wh...

If `S` is the sum to infinity of a G.P. whose first term is `'a'`, then the sum of the first `n` terms is
(A)  `S(1-a/S)^n`    (B)  `S[1-(1-a/S)^n]`   (C)  `a[1-(1-a/S)^n]`   (D)  `S[1-(1-S/a)^n]`

Text Solution

Verified by Experts

In a GP of the first term `a ` and common ratio `r`, sum `S` to the infinity is given by,
`S = a/(1-r)=> 1-r = a/S=> r = 1-a/S`.
`:.`Sum of n terms, `S_n = (a(1-r^n))/(1-r)`
`S_n = (a[1-(1-a/S)^n])/(a/S) = S[1-(1-a/S)^n]`
so, option `B` is the correct answer.
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