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 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_(1) a_(2))) + tan^(-1) ((d)/(1 + a_(2) a_(3))) + ...+ tan^(-1) ((d)/(1 + a_( - 1)a_(n)))] = ((n -1)d)/(1 + a_(1) a_(n))

If a_(1), a_(2), a_(3) are in arithmetic progression and d is the common diference, then tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))=

If a_1,a_2,a_3,…….a_n are in Arithmetic Progression, whose common difference is an integer such that a_1=1,a_n=300 and n in[15,50] then (S_(n-4),a_(n-4)) is

Let A_1 , A_2 …..,A_3 be n arithmetic means between a and b. Then the common difference of the AP is

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_1))

If a_1,a_2,……….,a_n are in H.P. then expression a1a2+a2a3+......+a_n-1an

Find the sum tan^-1 (1/(3+3.1+1^2))+tan^-1 (1/(3+3.2+2^2))+…+tan^-1 (1/(3+3n+n^2))

If tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2. 3))+.... +tan^(-1)(1/(1+n.(n+1)))=tan^(-1)theta, then find the value of thetadot