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.

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))

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

If y = 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)), x gt 0 and ((dy)/( dx))_(x=0)= ( - k )/( 1+ k) then the value of k is

If y = 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)), x gt 0 and ((dy)/( dx))_(x=0)= ( - k )/( 1+ k) then the value of k is

Find x if tan^(-1)(x) = tan^(-1)(1/2) + tan^(-1)(3/7)

If y = tan^(-1)(1/(1+x+x^2)) + tan^(-1)(1/(x^2+3x+3)) + tan^(-1)(1/(x^2+5x+7))+ …….. Up to n terms then find y'(0).

If tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/(x))=tan^(-1)(-7)+pi then x =

If tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/(x))=tan^(-1)(-7), then x is

If Y = "tan"^(-1)((1)/(1 + x + x^2)) + "tan"^(-1) (1/(x^2 + 3x + 3)) + "tan"^(-1)(1/(x^2 + 5x + 7)) + ….+ upto n term then y^1(0) =

Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3x^(2)))