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

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

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..

Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiation.

Find the sum of the series 31^3+32^3++50^3dot

Find the sum of the series ^15 C_0+^(15)C_1+^(15)C_2++^(15)C_7dot

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

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:

Find the sum of the series 1xxn+2(n-1)+3xx(n-2)++(n-1)xx2+nxx1.

Find the sum to n terms of the series 3//(1^2xx2^2)+5//(2^2xx3^2)+7//(3^2xx4^2)+dot