Sum the following series to infinity: `tan^(-1)1/(1+1+1^2)+tan^(-1)1/(1+2+2^2)+tan^(-1)1/(1+3+3^2)+`

tan^(-1)(1/2)+tan^(-1)(1/3)=?

tan^(-1)((1)/(2))+tan^(-1)((1)/(3))=

3(tan^(-1)1)/(2+sqrt(3))-(tan^(-1)1)/(2)=(tan^(-1)1)/(3)

tan^(-1)1+tan^(-1)2+tan^(-1)3=

tan^(-1)2-tan^(-1)1=tan^(-1)(1)/(3)

2tan^(-1)((1)/(3))+tan^(-1)((1)/(2))=

Find the sum of each of the following series: (i) tan^(-1)((1)/(x^(2)+x+1))+tan^(-1)((1)/(x^(2)+3x+3))+tan^(-1)((1)/(x^(2)+5X+7))+tan^(-1)((1)/(x^(2))+7x+13))...... upto n.