A 1999 IMO Chinese Team Selection Question

Algebra Level 5

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

Give your answer to 3 significant figures.

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