求数列计算方法,数学高手帮帮忙每年投资10000元,每年回报率为15%,连续投资60年,问5年后总金额有多少?参考答案：

a[1] = 0
a[n] = (a[n-1]+X)*(1+Y)
a[n] = (1+Y)a[n-1] + X + XY
设常数t使得
a[n] + t = (1+Y)(a[n-1] + t)
即要求 t + tY - t - 1 = X + XY 即 t = X/Y + X
(a[n] + t )/(a[n-1] +t) = 1 + Y
a[n] + t = (a[1] + t)(1+Y)^(n-1)
a[n] = {(1+Y)^(n-1) - 1}(X/Y + X)
N年后的总金额 S[N] = a[N+1] = {(1+Y)^N - 1}(X/Y + X)