If `S_1, S_2, ,S_n` are the sum of `n` term of `n` G.P., whose first term is 1 in each and common ratios are `1,2,3, ,n` respectively, then prove that `S_1+S_2+2S_3+3S_4+(n-1)S_n=1^n+2^n+3^n++n^ndot`

If S_1,S_2,S_3,...,S_n be the sums of first n terms of n G.P.'s whose first terms are each unity and the common ratios are 1, 2, 3,.....,n respectively, prove that S_1+S_2+2S_3+3S_4+.........+(n-1)S_n=1^n+2^n+3^n+....+n^n.

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) =

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 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 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_1,S_2 and S_3 are respectively the sums of n, 2n and 3n terms of an A.P, whose first term is a and common difference d, then find S_1,S_2 and S_3

If the sum of first n,2n,3n terms of an A.P. be S_1 , S_2 and S_3 respectively then prove that S_1+S_3=2S_2

If the sum of n , 2n , 3n terms of an AP are S_1,S_2,S_3 respectively . Prove that S_3=3(S_2-S_1)

If the sum of first n,2n,3n terms of an A.P. be S_1 , S_2 and S_3 respectively then prove that S_3=3(S_2-S_1)

The sum of n, 2n, 3n terms of an A.P. are S_1, S_2, S_3 respectively. Prove that S_3 = 3(S_2 - S_1)