The value of `tan^-1(1/3)+tan^-1(2/9)+tan^-1(4/33)+tan^-1(8/129)+....n` terms is:

Explanation

`T_r=tan^(-1)((2^(r-1))/(2^(2r-1)+1))`

`r_1=1/3`

`r_2=2/9`

`r_3=4/33`

`2^(r-1)=2*2^(r-1)-2^(r-1)=2^r-2^(r-1)`

`T_r=tan^(-1)((2^r*2^(r-1))/(1+2^r*2^(r-1)))`

`T_1=tan^(-1)(2)-tan(1)`

`T_2=tan^(-1)(4)-tan^(-1)(2)`

...