If the sum of the series `sum_(n=0)^oor^n ,|r|<1` is s , then find the sum of the series `sum_(n=0)^oor^(2n)` .

If the sum of the series Sigma_(n=0)^(oo) r^(n),|r|le 1 is s, then find the sum of the series Sigma_(n=0)^(oo) r^(2n),|r|le 1

Find the sum of the series sum_(r=1)^n rxxr !dot

The sum of the series sum_(n =8)^(17)1/((n + 2)(n + 3)) is equal to

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

In a geometric series , the first term is a and common ratio is r. If S_n denotes the sum of the n terms and U_n=Sigma_(n=1)^(n) S_n , then rS_n+(1-r)U_n equals

If the sum of the n terms of a G.P. is (3^(n)-1) , then find the sum of the series whose terms are reciprocal of the given G.P..

If C_r stands for nC_r , then the sum of the series (2(n/2)!(n/2)!)/(n !)[C_0^2-2C_1^2+3C_2^2-........+(-1)^n(n+1)C_n^2] ,where n is an even positive integer, is

If the sum of n terms of the series 2^(3) + 4^(3) + 6^(3) + ......... is 3528 then n =

If P_(r) stands for ""^(r)P_(r) then the sum of the series 1+ P_(1 )+ ""2 xxP_(2) + ""3 xxP_(3) + … + ""n xxP_(n) is:

If p+q=1, then show that sum_(r=0)^n r^2^n C_rp^r q^(n-r)=n p q+n^2p^2dot