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JEE Main202124 Feb 2021Morning ShiftMathematicsInverse Trigonometric FunctionsActual

lim n → ∞ tan ∑ r = 1 n tan - 1 1 1 + r + r 2 is equal to_______.

Correct answer

0

Step-by-step solution

lim n → ∞ tan ∑ r = 1 n tan - 1 1 1 + r r + 1 = lim n → ∞ tan ∑ r = 1 n tan - 1 r + 1 - r 1 + r r + 1 = tan lim n → ∞ ∑ r = 1 n tan - 1 r + 1 - tan - 1 r = tan lim n → ∞ tan - 1 n + 1 - π 4 = tan π 4 = 1

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