Find the sum `1^(2) + (1^(2)+2^(2))+ (1^(2)+2^(2)+3^(2))+ cdots` up to 22 nd term.

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 .

Find the sum 1+(1)/(1+2) + (1)/(1+2+3) + cdots+ (1)/(1+2+3+cdots+ n )

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

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

If S = (2^(2)-1)/(2)+(3^(2)-2)/(6)+(4^(2)-3)/(12)+ cdots upto 10 terms then S is equal to

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

If |a| lt 1 and |b| lt 1 then the sum of the series 1+(1+a) b+(1+a+ a^(2))b^(2)+ (1+a+a^(2)+a^(3)) b^(3)+cdots is

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 of (x+2)^(n-1)+ (x+2)^(n-2) (x+1) + (x+2)^(n-3) (x+1)^(2) + cdots + (x+1)^(n-1) is equal to