Kata

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 or to another number?

Task

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

Your result should be within 10^-6 of the expected one.

Remark

Keep in mind that factorials grow rather rapidly, and you need to handle large inputs.

Hint

You could try to simplify the expression.