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cot^-1(2^2 + 1/2) +cot^-1(2^3 + 1/2^2) + cot^-1(2^4 + 1/2^3) +... infinity find its value?

cot^-1(2^2 + 1/2) +cot^-1(2^3 + 1/2^2) + cot^-1(2^4 + 1/2^3) +... infinity
find its value?
 

Grade:12

1 Answers

Lab Bhattacharjee
121 Points
5 years ago
\text{HINT: }\cot^{-1}\left(2^n+\dfrac1{2^{n-1}} \right)=\cot^{-1}\left(\dfrac{2^n\cdot2^{n-1}+1}{2^n-2^{n-1}} \right)\\ =\cot^{-1}\dfrac1{2^n}-\cot^{-1}\dfrac1{2^{n-1}}

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