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AoPS Wiki talk:Problem of the Day/June 17, 2011

Revision as of 13:12, 17 June 2011 by Hydroxide (talk | contribs) (→‎Solution)
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Problem

AoPSWiki:Problem of the Day/June 17, 2011

Solution

$\frac{1^{3}+2^{3}+3^{3}+\cdots+x^{3}}{1+2+3+\cdots+x}=\frac{(1+2+3+\cdots+x)^2}{1+2+3+\cdots+x}=1+2+3+\cdots+x$


$1+2+3+\cdots+x=\frac{x\cdot(x+1)}{2}$ Subbing in the value of $x$ we get,$\frac{9001\cdot9002}{2}=\boxed{40513501}$

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