Question

If a₁, a₂, ..........a_n+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) \(tan^{-1}\frac{(n+1)d}{1 - a_1a_{n+1}}\)

Answer 1

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