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 sum to n terms of the series 1+2 (1+(1)/(n))+3 (1+(1)/(n))^(2)+ cdots is given by

Find the sum to infinity of the sequence 1,1/3,1/9,………

If the sum to infinity of the series 1 + 2r + 3r^(2) + 4r^(3)+ cdots is 9/4 then value of of r is

Find the sum to infinity of the series 1-3x+ 5x^(2)+7x^(3)+ cdots oo when |x| lt 1 .

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

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

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

Find the sum to n terms of the series 3+15+35+63+ cdots .

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

If S denotes the sum to infinity and S_(n) , denotes the sum of n terms of the series 1+(1)/(2)+(1)/(4) + (1)/(8)+ cdots , such that S-S_(n) lt (1)/(100) , then the least value of n is