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Real Analysis : Proof using an Integral and Mean Value Theorem

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For numbers a1,....,an, define
p(x) = a1x +a2x^2+....+anx^n for all x. Suppose that:

(a1)/2 + (a2)/3 +....+ (an)/(n+1) = 0

Prove that there is some point x in the interval (0,1) such that p(x) = 0

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Solution Summary

An integral and Mean Value Theorem are used to provide a real analysis proof.

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