Find the sum to infinity of the series `1^2+2^2x+3^2x^2+oodot`

Find the sum to ininity of the series 1-3x+5x^2+7x^3+..... oo when Ix| <1.

Find the sum to n terms of the series 1^2+2^2+3^2-4^2+5^2-6^2+. . . .

If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then value of r is 1//2 b. 1//3 c. 1//4 d. none of these

Find the sum of the series 1^2+3^2+5^2+ ton terms.

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

Find the sum of the firt 40 terms of the series 1^(2) -2^(2) + 3^(2) - 4^(2) +……….

Find the sum to n terms of each of the series in 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ...

If the sum to infinty of the series , 1+4x+7x^(2)+10x^(3)+…. , is (35)/(16) , where |x| lt 1 , then 'x' equals to

If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+oo is (44)/9 , then find ddot