题目235：一种算术几何序列

欧拉计划

An Arithmetic Geometric sequence

Given is the arithmetic-geometric sequence u(k) = (900-3k)r^k-1.
Let s(n) = Σ_k=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.

题目：

假设算术几何序列 u(k) = (900-3k)r^k-1。

设 s(n) = Σ_k=1...nu(k).

求 r 的值，使得 s(5000) = -600,000,000,000。

给出你的答案并精确到第 12 位小数。