Find the sum of the series :
`(1)/(2) + (1)/(3^(2))+(1)/(2^(3))+(1)/(3^(4))+(1)/(2^(5))+(1)/(3^(6))+ cdots oo`

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

Calculate the following . Write them as products. i) (1)/(4) of (1)/(2) ii) (1)/(2) of (1)/(4) iii) (1)/(5) of (1)/(3) iv) (1)/(3) of (1)/(5) v) (1)/(6) . of (1)/(3) vi) (1)/(3) of (1)/(6)

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

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 this series. 1/(1xx2)+1/(2xx3)+1/(3xx4)+......

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

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