Find the sum of the infinite series `(1)/(9) + (1)/(18) +(1)/(30) +(1)/(45)+(1)/(63)+cdots.`

The sum of the infinite series 1, 1/3, 1/9 ,……… Is…………….

Find the sum of the series (1^(3))/(1) + (1^(3)+2^(3))/(1+3)+(1^(3)+2^(3)+3^(3))/(1+3+5)+ cdots up to n terms .

For x gt 0 the sum of the series (1)/(1+x) - ((1-x))/((1+x)^(2))+ ((1-x)^(2))/((1+x)^(3))- cdots oo is equal to

Find the sum of the series ""^(15)C_(0)+^(15)C_(1)+^(15)C_(2)+….+^(15)C_(7) .

Find the sum of the series 31^(3) + 32^(3) + cdots +50^(3) .

Find the sum to n terms of the series 1//(1xx2) + 1//(2xx3) + 1//(3xx4) + cdots + 1//n(n+1).

Find the sum to n terms of the series 1//(1xx3)+1//(3xx5)+1//(5xx7)+ cdots .

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

The maximum sum of the series 20 +19(1)/(3)+18 (2)/(3) + cdots is

Find the sum of n terms of the series 1 + 4/5 + 7//5^(2) + 10//5^(3)+ cdots