Evaluate lim n → ∞ n 1 ∑ r = 0 n tan − 1 ( 1 + r + r 2 ) .

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsSummation of seriesHard2 minQB

MathematicsHardsingle choice

Evaluate $lim_{n \to \infty} \frac{1}{n} \sum_{r = 0}^{n} tan^{- 1} (1 + r + r^{2})$ .

Answer:

Solution:

Use $tan^{- 1} (1 + r + r^{2}) = π /2 - [tan^{- 1} (r + 1) - tan^{- 1} r]$ ; the correction divided by $n$ vanishes.

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Summation of series

⏱ 2mℹ️ Source: QB

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