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OpenStudy (anonymous):
Assume a0 a1 a2 … an belong to R and satisfy the equation a0 + a1 /2+ a2 /3+…+ an /(n+1)=0 prove that the equation a0+a1 x+a2 x^2+…+an x^n=0 has at least a solution x belong to open interval 0 to 1
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