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

Find the sum of the series e^(x-(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ...

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

The sum of the series (1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+... is

Find the sum to n terms of the series: (1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)+2^(4))+(3)/(1+3^(2)+3^(4))+

Find the sum of the series 1+ (1+2) + (1+2+3) + (1+2 + 3 +4)+ … + (1+2+3+… + 20) .

Find the sum to n terms of the series (1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)+2^(4))+(3)/(1+3^(2)+3^(4))+ that means t_(r)=(r)/(r^(4)+r^(2)+1) find sum_(1)^(n)

The sum of the series 1+ 2/3+ (1)/(3 ^(2)) + (2 )/(3 ^(3)) + (1)/(3 ^(4)) + (2)/(3 ^(5)) + (1)/(3 ^(6))+ (2)/(3 ^(7))+ …… upto infinite terms is equal to :