Given the sum of the first n terms of the sequence {an}, Sn = + 2n, TN = 1 / (A1A2) + 1 / (a2a3) + 1 / (a3a4) +... + 1 / (Anan + 1), find TN

Given the sum of the first n terms of the sequence {an}, Sn = + 2n, TN = 1 / (A1A2) + 1 / (a2a3) + 1 / (a3a4) +... + 1 / (Anan + 1), find TN

When n = 1, A1 = S1 = 1 & # 178; + 2 × 1 = 3N ≥ 2, an = SN-S (n-1) = n & # 178; + 2n - [(n-1) &# 178; + 2 (n-1)] = 2n + 1n = 1, A1 = 2 × 1 + 1 = 3, the general term formula satisfying the general term formula sequence {an} is an = 2n + 11 / [ana (n + 1)] = 1 / [(2n + 1) (2 (n + 1) + 1)] = (1 / 2)