if `S_n` denotes the sum of `n` terms of a G.P whose first term is a and common ratio is r then find the sum of `S_1 , S_3,S_5..........,S_2n-1`

If S_n denotes the sum of n terms of a G.P. whose first term and common ratio are a and r respectively, then : S_1 +S_3+S_5+.....+S_(2n-1)= (an)/(1-r)-(ar(1-r^(2n)))/((1-r)^2 (1+r)) .

If S_(n) denotes the sum of n terms of a G.P., whose common ratio is r, then (r-1) (dS_(n))/(dr) =

If S_n denotes the sum of n terms of an A.P. whose first term is a, and the common difference is d Find: = Sn - 2Sn + S(n +2) .

If S is the sum to infinite terms of a G.P whose first term is 'a', then the sum of the first n terms is

If S_(n) denotes the sum fo n terms of a G.P. whose first term and common ratio are a and r respectively then show that: S_(1)+S_(3)+S_(5)+……..+S_(2n)-1=(an)/(1-r)-(ar(1-r^(2n)))/((1-r^(2))

If S_n represents the sum of n terms of a G.P. whose first term and common ratio are a and r respectively. Prove that : S_1 +S_2+S_3+.....+S_(m)= (am)/(1-r)-(ar(1-r^(m)))/((1-r)^2) .

If S is the sum to infinite terms of a G.P.whose first term is 1. Then the sum of n terms is

If S_(n) denote the sum to n terms of an A.P. whose first term is a and common differnece is d , then S_(n) - 2S_(n-1) + S_(n-2) is equal to

If S_(n) denotes the sum of first n terms of an A.P whose first term is a and (S_(nx))/(S_(x)) is independent of x then S_(p)=