if `s_n`, denotes the sum of n terms of a GP whose first term and common ratio are `a` and `r` respectively. then `S_1+S_2.........+S_n` is

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 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_(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 G.P whose first term and common ratio are a and r respectively, then s_(1) + s_(2) + s_(3) + …+ s_(n) =

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: The sum of product of first n terms of the G.P. taken two at a time in (A) (r+1)/r S_nS_(n-1) (B) r/(r+1)S_n^2 (C) r/(r+1)S_nS_(n-1) (D) none of these

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: The sum of product of first n terms of the G.P. taken two at a time in (A) (r+1)/r S_nS_(n-1) (B) r/(r+1)S_n^2 (C) r/(r+1)S_nS_(n-1) (D) none of these

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_3+..+S_n= (A) (na)/(1-r)-(ar(1-r^n))/((1-r)^2 (B) (na)/(1-r)-(ar(1+r^n))/((1+r)^2 (C) (na)/(1-r)-(a(1-r^n))/((1-r)^2 (D) none of these

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_2+..+S_n= (A) (na)/(1-r)-(ar(1-^n))/((1-r)^20 (B) (na)/(1-r)-(ar(1+^n))/((1+r)^20 (C) (na)/(1-r)-(a(1-^n))/((1-r)^20 (D) none of these

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_(2)n-1

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