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[" 4.Sum the following series: "],[qquad...

[" 4.Sum the following series: "],[qquad tan^(-1)(1)/(3)+tan^(-1)(2)/(9)+tan^(-1)(4)/(33)+...+tan^(-1)(2^(n-1))/(1+2^(2n-1))]

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tan^(-1)(1)/(4)+tan^(-1)(2)/(9)=tan^(-1)(1)/(2)

tan^(- 1)(1/4)+tan^(- 1)(2/9)=1/2tan^(- 1)(4/3)

tan^(- 1)(1/4)+tan^(- 1)(2/9)=1/2tan^(- 1)(4/3)

tan^(-1)((1)/(4))+tan^(-1)((2)/(9))=tan^(-1)((1)/(2))

Tan^(-1)(1/3)+Tan^(-1)(2/9)+Tan^(-1)(4/33)+…… infty

Prove that "tan"^(-1)(1)/(4) +"tan"^(-1)(2)/(9) =(1)/(2)"tan"^(-1)(4)/(3) .

Prove that 2(tan^(-1)1/4+tan^(-1)2/9)=tan^(-1)4/3 .

Prove that tan^(-1)""(1)/(4)+tan^(-1)""(2)/(9)=(1)/(2)tan^(-1)""(4)/(3)

tan^(-1)((3)/(n))+tan^(-1)((4)/(n))=(pi)/(2)