Find the sum of the series :
`(sqrt(2+1))+1+(sqrt(2)-1)+ cdots oo`

Find the sum of the series 1.n + 2 .(n-1) + 3.(n-2) + cdots + ( n-1) .2 + n.1.

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

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

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

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

Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4

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

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