The known sequence {an} satisfies A1 = 1, an = a1 + 2A2 + 3a3 + +(n-1) an-1, then when n ≥ 2, the general term an = () A. n!2B. (n+1)!2C. n!D. （n+1）!

The known sequence {an} satisfies A1 = 1, an = a1 + 2A2 + 3a3 + +(n-1) an-1, then when n ≥ 2, the general term an = () A. n!2B. (n+1)!2C. n!D. （n+1）!

From an = a1 + 2A2 + 3a3 + +(n-1) an-1 (n ≥ 2), Nan + an = a1 + 2A2 + 3a3 + +If (n-1) an-1 + Nan (n ≥ 2), (n + 1) · an = an + 1 (n ≥ 2), then an + 1An = n + 1 (n ≥ 2), and A1 = 1, A2 = 1, a3a2 = 3, a4a3 = 4 The cumulative result is an = n! 2

If the sequence {an} satisfies a1 + 2A2 + 3a3 +... + Nan = n (n + 1) (n + 2), then an = process detail point

Because a1 + 2A2 + 3a3 +... + Nan = n (n + 1) (n + 2),
So a1 + 2A2 + 3a3 +... + (n-1) a (n-1) = (n-1) n (n + 1),
By subtracting the two formulas, Nan = n (n + 1) [(n + 2) - (n-1)]
So an = 3 (n + 1)