065 Convergents of e.sf

#!/usr/bin/ruby

# Author: Daniel "Trizen" Șuteu
# License: GPLv3
# Website: https://github.com/trizen

# Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.

# https://projecteuler.net/problem=65

# Runtime: 0.112s

func e(n, i=1) {

    return 0 if (i >= n)

    1/(
        1 + 1/(
            2*i + 1/(
                1 + e(n, i+1)
            )
        )
    )
}

var n = 100
var frac = 2+e(int(n/3 + 1))

say frac.numerator.sumdigits