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
A proof is provided for a real analysis problem using summation integrals.