A 1999 IMO Chinese Team Selection Question

Algebra Level 5

For non-negative real numbers x1,x2,...,xn x_{1},\: x_{2},\: ...,\: x_{n} , which satisfy x1+x2+...+xn=1 x_{1}+x_{2}+...+x_{n}=1 , find the largest possible value of j=1n(xj4xj5)\displaystyle \sum_{j=1}^{n}(x_{j}^{4}-x_{j}^{5}) .

Give your answer to 3 significant figures.

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