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the powers of the roots of a cubic

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November 15, 2009
algebrapolynomial

Problem Statement

The three roots of the cubic 30 x^3 \minus{} 50x^2 \plus{} 22x \minus{} 1 are distinct real numbers between 0 0 and 1 1. For every nonnegative integer n n, let sn s_n be the sum of the n nth powers of these three roots. What is the value of the infinite series s_0 \plus{} s_1 \plus{} s_2 \plus{} s_3 \plus{} \dots \, ?
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