# 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.

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