python算法：Going to zero or to infinity?

Consider the following numbers (where n! is factorial(n)):

u1 = (1 / 1!) * (1!)
u2 = (1 / 2!) * (1! + 2!)
u3 = (1 / 3!) * (1! + 2! + 3!)
un = (1 / n!) * (1! + 2! + 3! + ... + n!)
Which will win: 1 / n! or (1! + 2! + 3! + ... + n!)?

Are these numbers going to 0 because of 1/n! or to infinity due to the sum of factorials?

Task
Calculate (1 / n!) * (1! + 2! + 3! + ... + n!) for a given n, where n is an integer greater or equal to 1.

To avoid discussions about rounding, return the result truncated to 6 decimal places, for example:

1.0000989217538616 will be truncated to 1.000098
1.2125000000000001 will be truncated to 1.2125

我的解法：

def going(n):
    nnn=1
    sum=0
    for i in range(1,n+1):
        nnn*=i
        sum+=nnn
    return (1/nnn)*sum