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

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

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

Find the sum to n terms of the G.P. x^3,x^5,x^7,…(xne+-1)

Find the sum of coefficients in (1+x-3x^(2))^(4163)

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

Let x , |x-1| and |x + 1| be the first three terms of a G.P. then sum of the series (1)/(x)+ (1)/(|x-1|)+(1)/(|x+1|)+cdots oo is equal to

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