Sum the series `tan^-1 (x/(1+1*2x^1))+tan^-1 (x/(1+2*3x^2))+…+tan^-1 (x/(1+n*(n+1)x^2))`

Find the sum tan^-1 (x/ (1+1.2x^2))+tan^-1 (x/(1+2.3x^2))+…+tan^-1 (x/(1+n(n+1)x^2)) xgt0

[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]

AA n in N,x in R,tan^(-1)[(x)/(1.2+x^(2))]+tan^(-1)[(x)/(2.3+x^(2))]+......+tan^(-1)[(x)/(n(n+1)+x^(2))]=

If: tan^(-1)((x-1)/(x+1))+ tan^(-1)((2x-1)/(2x+1)) = tan^(-1) (23/36) . Then: x=

tan^(-1)((1)/(1+2x))+tan^(-1)((1)/(1+4x))=tan^(-1)((2)/(x^) (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.

tan ^ (-1) (x + (2) / (x))-tan ^ (-1) ((4) / (x)) = tan ^ (-1) (x- (2) / (x))