Given is the arithmetic-geometric sequence u(k) = (900-3k)rk-1.
Let s(n) = Σk=1...nu(k).
Find the value of r for which s(5000) = -600,000,000,000.
Give your answer rounded to 12 places behind the decimal point.
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK