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)1/3+(tan^- 1)2/9+....+(tan^- 1)(2^(n-1))/(1+2^(2n-1))+...... oo

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

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: 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

tanx + tan2x + tan3x = tanx tan2x tan3x

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

Find the sum n terms of seires tan theta+1/2tan(theta/2 )+1/(2^2)tan(theta/(2^2))+1/(2^3)tan(theta/(2^3))+....