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An Arithmetic Geometric sequence

Problem 235

Published on Saturday, 7th March 2009, 05:00 am; Solved by 3241

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.