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0 votes
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in Algebra by (53.3k points)

If a1, a2, ..........an+1 are in A.P with common difference d, then \(\sum\limits_{r =1}^n tan^{-1}\frac d{1 + a_ra_{r + 1}}\)

(a) \(tan^{-1} \frac{nd}{1 + a_1a_{n+1}}\)

(b) \(tan^{-1} \frac{(n +1)d}{1 + a_1a_{n+1}}\)

(c) \(tan^{-1} \frac{(n -1)d}{1 - a_1a_{n+1}}\)

(d) \(tan^{-1} \frac{(n -1)d}{1 + a_1a_{n+1}}\)

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1 Answer

+1 vote
by (53.5k points)

Correct option is (a) \(tan^{-1} \frac{nd}{1 + a_1a_{n+1}}\) 

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