If S is the sum to infinity of a G.P.,whose f | vedclass

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(B) Let $r$ be the common ratio of the $G.P.$The sum to infinity $S$ is given by $S = \frac{a}{1 - r}$.Rearranging for $r$,we get $1 - r = \frac{a}{S}

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$S\left[ {1 - {{\left( {1 - \frac{a}{S}} \right)}^n}} \right]$

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(B) Let $r$ be the common ratio of the $G.P.$The sum to infinity $S$ is given by $S = \frac{a}{1 - r}$.Rearranging for $r$,we get $1 - r = \frac{a}{S}$,which implies $r = 1 - \frac{a}{S}$.The sum of the first $n$ terms $S_n$ of a $G.P.$ is given by $S_n = \frac{a(1 - r^n)}{1 - r}$.Substituting $S = \frac{a}{1 - r}$ and $r = 1 - \frac{a}{S}$ into the formula:$S_n = S(1 - r^n) = S\left[ {1 - {{\left( {1 - \frac{a}{S}} \right)}^n}} \right]$.

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

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