If `a_1,a_2,a_3, a_n` are in arithmetic progression with common difference `d ,` then evaluate the following expression: `tan{tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a^2a_3))+tan^(-1)(d/(1+a_3a_4))++tan^(-1)(d/(1+a_(n-1)a_n))}`

If a_(1),a_(2),a_(3),...a_(n) are in arithmetic progression with common difference d, then evaluate the following expression: tan{tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a^(2)a_(3)))+tan^(-1)((d)/(1+a_(3)a_(4)))+...+tan^(-1)((d)/(1+a_(n-1)a_(n)))}

If a_(1),a_(2),a_(3),...,a_(n) is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan^(-1)(d/(1+a_(1)a_(2)))+tan^(-1)(d/(1+a_(2)a_(3)))+...+tan^(-1)(d/(1+a_(n-1)*a_(n)))]

If a_(1), a_(2), a_(3), …..a_(n) is an arithmetic progression with common difference d. Prove that tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+…+tan^(-1)((d)/(1+a_(n)a_(n-1)))]=(a_(n)-a_(1))/(1+a_(1)a_(n))

If a_1,a_2,a_3 ,….""a_n is an aritmetic progression with common difference d. prove that tan [ tan ^(-1) ((d)/( 1+ a_1a_2))+ tan^(-1) ((d)/(1+a_2a_3))+…+((d)/(1+a_n a_( n-1))) ] = (a_n -a_1)/(1 +a_1 a_n )

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then prove that "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+tan^(-1)(d/(1+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then prove that "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+tan^(-1)(d/(11+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then prove that "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+......+tan^(-1)(d/(1+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+...+tan^(-1)(d/(1+a_(n-1)a_n))]=

If a_(1),a_(2),a_(3),a_(n) is an A.P.with common difference d, then prove that tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+tan^(-1)((d)/(1+a_(n-1)a_(n)))]=((n-1)d)/(1+a_(1)a_(n))