1.

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

Answer» `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)`
`T_3=tan^(-1)(8)-tan^(-1)(4)`
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`T_n=tan^(-1)(2^n)-tan^(-1)(2^(n-1))`
`T_1+T_2+t_3+...+T_n=tan^(-1)2^n-pi/4`
option 1 is correct.


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