The value of cot-1(22 + 1/2) + cot-1(23 + 1/22) + ……∞ is equal to tan-1 λ, then the value of λ is equal to __________
The value of cot-1(22 + 1/2) + cot-1(23 + 1/22) + ……∞ is equal to tan-1 λ, then the value of λ is equal to __________
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1 Answer
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T? = cot? ¹ (2²? ¹ + 1/2? ) = cot? ¹ (1 + 2²? ¹)/2? ) = tan? ¹ (2? / (1 + 2²? ¹)
T? = tan? ¹ (2? ¹ - 2? ) / (1 + 2? ¹ . 2? ) = tan? ¹ (2? ¹) – tan? ¹ (2? )
S∞ = π/2 - tan? ¹ (2) = cot? ¹ (2) = tan? ¹ (1/2)
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