| 12345678910111213141516171819202122232425 |
- \\ Pari/GP
- \\ Daniel "Trizen" Șuteu
- \\ Date: 27 September 2017
- \\ https://github.com/trizen
- \\ https://projecteuler.net/problem=235
- \\
- \\ s(n) = sum((900-3k)*x^(k-1), {k=1..n})
- \\
- \\ We can easily derive a closed-form using Wolfram|Alpha:
- \\ http://www.wolframalpha.com/input/?i=sum((900-3k)*r%5E(k-1),+%7Bk%3D1..n%7D)
- \\
- \\ we get:
- \\ s(n) = (-3 * (n - 300) * x^(n + 1) + 3 * (n - 299) * x^n - 900*x + 897)/(x - 1)^2
- \\
- \\ Where, for `n=5000`, we have:
- \\ s(5000) = (-14100 * x^5001 + 14103 * x^5000 - 900*x + 897)/(x - 1)^2
- \\
- \\ Problem asks solving for `x`, such that `s(5000) = -600000000000`.
- \\
- print(solve(x=-1,2,(-14100 * x^5001 + 14103 * x^5000 - 900*x + 897)/(x - 1)^2 + 600000000000));
|
