It is known that the sum of the first n terms of the sequence {an} is Sn, and A1 = 1, an + 1 = half times Sn (n = 1.2.3.) (1) find the general formula of the sequence {an} (2) When BN = log 3 / 2 (3an + 1), prove: the sum of the first n terms of the sequence {BN * BN + 1 / 1}, TN = 1 + n / n

It is known that the sum of the first n terms of the sequence {an} is Sn, and A1 = 1, an + 1 = half times Sn (n = 1.2.3.) (1) find the general formula of the sequence {an} (2) When BN = log 3 / 2 (3an + 1), prove: the sum of the first n terms of the sequence {BN * BN + 1 / 1}, TN = 1 + n / n

∵ a (n + 1) = 1 / 2 * Sn, A1 = 1 ∵ A2 = 1 / 2 * A1 = 1 / 2A3 = 1 / 2 * S2 = 1 / 2 (a1 + A2) = 3 / 4 when n ≥ 2, an = 1 / 2 * s (n-1) ∵ a (n + 1) - an = 1 / 2 * sn-1 / 2 * s (n-1) = 1 / 2 * [SN-S (n-1)] = 1 / 2 * an ∵ a (n + 1) = 3 / 2 * ana (n + 1) / an = 3 / 2 ∵ A2 = A1 = 1 / 2 ∵ {an} is an equal ratio sequence from the second term