$$tan$$−$$111+(1)(2)+$$$$tan$$−$$111+(2)(3)+$$...............$$+$$$$tan$$−$$111+(n$$−$$1)(n)=$$

Correct option is 4tan−1(n−1n+1)

Questions

$\tan^{- 1} (\frac{1}{1 + (1) (2)}) + \tan^{- 1} (\frac{1}{1 + (2) (3)}) + ............... + \tan^{- 1} (\frac{1}{1 + (n - 1) (n)}) =$

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detailed solution

Correct option is D

We have tan-111+12+an-111+23+....+an-111+n-1n =tan-12-11+12+an-13-21+23+....+an-1n-n-11++n-1n =tan-12-tan-11+tan-13-tan-12+...+tan-1n-tan-1n-1 =tan-1n-tan-11 =tan-1n-11+n

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tan−111+(1)(2)+tan−111+(2)(3)+...............+tan−111+(n−1)(n)=

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$\tan^{- 1} (\frac{1}{1 + (1) (2)}) + \tan^{- 1} (\frac{1}{1 + (2) (3)}) + ............... + \tan^{- 1} (\frac{1}{1 + (n - 1) (n)}) =$