[" 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) be the sum of first n terms of a G.P. whose common ratio is r, then show that, (r-1)(dS_(n))/(dr)=(n-1)S_(n)-nS_(n-1)

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 an A.P. whose common difference is d and first term is a,find S_(n)-2S_(n-1)+S_(n-2)

If S_(n) is the sum of a G.P. to n terms of which r is the common ratio, then : (r-1)*(d)/(dr)(S_(n))+nS_(n-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) 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 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 denotes the sum of n terms of an A.P. whose common difference is d and first term is a, find S_n-2S_(n-1)+S_(n-2)