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Flag Trigonometry> cot^-1(2^2 + 1/2) +cot^-1(2^3 + 1/2^2) + ...
question mark

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

Aman raj , 10 Years ago
Grade 12
anser 1 Answers
Lab Bhattacharjee
\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}}
Last Activity: 10 Years ago
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