Let f (x) satisfy 2F (x) - f (1 / x) = 4x-2 / x + 1, sequence {an} and {BN} satisfy A1 = 1, a (n + 1) - 2An = f (n), BN = a (n + 1) - an Finding the analytic expression of F (x) The general term formula of BN Is to compare the size of 2An and BN, and prove that

Let f (x) satisfy 2F (x) - f (1 / x) = 4x-2 / x + 1, sequence {an} and {BN} satisfy A1 = 1, a (n + 1) - 2An = f (n), BN = a (n + 1) - an Finding the analytic expression of F (x) The general term formula of BN Is to compare the size of 2An and BN, and prove that

2F (x) - f (1 / x) = 4x-2 / x + 1. (formula 1) in Formula 1, let 1 / X replace x, where 2F (1 / x) - f (x) = 4 / x-2x + 1. (formula 2) (formula 1) * 2 + (formula 2), f (x) = 2x + 1______________________________________________ A (n + 1) - 2A (n) = f (n) = 2n + 1, that is: a (n + 1) + 2 (n + 1) + 3 = 2 (a

In the sequence {an}, two adjacent terms an and an + 1 are two of the equation x2 + 3nx + BN = 0. Given that A10 = - 17, then the value of B51 is equal to ()
A. 5800B. 5840C. 5860D. 6000

∵ an, an + 1 are two of the equations x2 + 3nx + BN = 0, ∵ an + an + 1 = - 3N, an · an + 1 = BN. ∵ an + 2-An = (an + 2 + an + 1) - (an + 1 + an) = - 3 (n + 1) - (- 3n) = - 3 ∵ A1, A3 , A2N + 1 and A2, A4 , an are all arithmetic sequences with tolerance of - 3,... A52 = A10 + 21 (- 3) = - 80