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Calculate the value over sum 2^n * x_n

Source: IMO Longlist 1989, Problem 38

September 18, 2008
inductionalgebra solvedalgebra

Problem Statement

A sequence of real numbers x0,x1,x2,… x_0, x_1, x_2, \ldots is defined as follows: x_0 \equal{} 1989 and for each n≥1 n \geq 1 x_n \equal{} \minus{} \frac{1989}{n} \sum^{n\minus{}1}_{k\equal{}0} x_k. Calculate the value of \sum^{1989}_{n\equal{}0} 2^n x_n.
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