goingZeroOrInfinity.md

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 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.

• 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

Remark

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

Hint

• You could try to simplify the expression.

Solution:

function going(n) {
  let res = 1,
    acc = 1;
  for (let i = n; i > 1; i--) {
    acc /= i;
    res += acc;
  }
  return Number(String(res).slice(0, 8)); 
}

console.log(going(5)); // 1.275
console.log(going(6)); // 1.2125
console.log(going(7)); // 1.173214