235 An Arithmetic Geometric sequence.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# License: GPLv3
# Date: 27 September 2017
# https://github.com/trizen

# https://projecteuler.net/problem=235

# Runtime: 0.162s

const n = 5000
const u = -600000000000

var r1 = 1
var r2 = 2

while (r1 <= r2) {

    var r = ((r1+r2) / 2)
    var v = (((3*(n-299) * r**n) - (3*(n-300) * r**(n+1)) - 900*r + 897) / (r - 1)**2 - u)

    if (abs(r1 - r2) < 1e-14) {
        printf("%.12f\n", r1)
        break
    }

    if (v > 0) {
        r1 = r
    }
    else {
        r2 = r
    }
}