Find the sum of the series `tanx +2tan2x+2^2tan2^2 x+…=2^(n-1)tan2^(n-1)x`

Find the sum of the series tan^(-1)((1)/(2))+tan^(-1)((1)/(2))+tan^(-1)((1)/(18))+tan^(-1)((1)/(32))+

Find the sum: tan x + 1/2 tan x/2+ 1/2^(2) tan x/2^(2) +.....+1/2^(n-1) tan x/2^(n-1)

Find the sum of the series : (tan^(-1))(1)/(3)+(tan^(-1))(2)/(9)+...+(tan^(-1))(2^(n-1))/(1+2^(2n-1))+......oo

Find the sum to infinite terms of the series tan^(-1)((1)/(3))+tan^(-1)((2)/(9))+"........."+tan^(-1)((2^(n-1))/(1+2^(2n-1)))+"......" .

If the sum of the series tan^(-1)3+tan^(-1)(9/2)+tan^(-1)(33/4)+...... to n terms = ((2n+1)pi)/(A)+B tan^(-1)(2^(n)) then (A+B) is equal to

Evaluate int tanx tan 2x tan 3x dx .

Prove that tan(2tan^(-1)x)=2tan(tan^(-1)x+tan^(-1)x^(3))

tan4x = (4tanx (1-tan^2x))/(1-6tan^2x+tan^4x)

Find the sum of the series 1+2x+3x^(2)+(n-1)x^(n-2) using differentiation.