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    Real Analysis : Proof using Summation Integrals

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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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    Ok, we have:

    Now let's take the integral of this expression ...

    Solution Summary

    A proof is provided for a real analysis problem using summation integrals. The expert proves there is some point within an interval.