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 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 P_(n) is the sum of a G.P. upto n terms (n>=3), then prove that (1-r)(dP_(n))/(dr)=(1-n)P_(n)+nP_(n-1), where r is the common ratio of G.P.

If P_n is the sum of a GdotPdot upto n terms (ngeq3), then prove that (1-r)(d P_n)/(d r)=(1-n)P_n+n P_(n-1), where r is the common ratio of GdotPdot

If P_n is the sum of a GdotPdot upto n terms (ngeq3), then prove that (1-r)(d P_n)/(d r)=(1-n)P_n+n P_(n-1), where r is the common ratio of GdotPdot

If P_n is the sum of a GdotPdot upto n terms (ngeq3), then prove that (1-r)(d P_n)/(d r)=(1-n)P_n+n P_(n-1), where r is the common ratio of GdotPdot

If P_n is the sum of a GdotPdot upto n terms (ngeq3), then prove that (1-r)(d P_n)/(d r)=(1-n)P_n+n P_(n-1), where r is the common ratio of GdotPdot

Prove that the sum of n terms of GP with first term a and common ratio r is given by S_(n)=a(r^(n)-1)/(r-1)

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 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