Algebra · Polynomial evaluation · Alternating sum · Geometric series
The polynomial \(P\) is given by
\[ P(x) = x^{2000} - 2000x^{1999} + 2000x^{1998} - \cdots + 2000x^{2} - 2000x + 2000 . \]
Compute \(P(1999)\).
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Serbian Regional Competition (Okruzno takmicenje) 1999, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source