It is known that {an} is an arithmetic sequence, tolerance D ≠ 0, an ≠ 0 (n ∈ n +), and a (k) x ^ 2 + 2A (K + 1) x + a (K + 2) = 0 (K ∈ n +) (1) Proof: when k takes different natural numbers, the equation has a common root (2) If the roots of different equations are x1, X2 ,Xn,… To prove the sequence 1 / (x1 + 1), 1 / (x2 + 1) ,1/(Xn+1)… Is an arithmetic sequence

It is known that {an} is an arithmetic sequence, tolerance D ≠ 0, an ≠ 0 (n ∈ n +), and a (k) x ^ 2 + 2A (K + 1) x + a (K + 2) = 0 (K ∈ n +) (1) Proof: when k takes different natural numbers, the equation has a common root (2) If the roots of different equations are x1, X2 ,Xn,… To prove the sequence 1 / (x1 + 1), 1 / (x2 + 1) ,1/(Xn+1)… Is an arithmetic sequence

It is proved that (1) ∵ {an} is a sequence of arithmetic numbers, ∵ 2A (K + 1) = a (k) + a (K + 2), so the equation a (k) x ^ 2 + 2A (K + 1) x + a (K + 2) = 0 can be changed to [a (k) x + a (K + 2)] (x + 1) = 0, ∵ when k takes different natural numbers, the original equation has a common root - 1 (2) the different roots of the original equation are x (k) = - [a (K + 2)] / a (k) = - [a (k) + 2D] /