Openly Hard

Algebra Level 5

Determine the largest integer \(n\) such that \[\sum_{i=1}^n{x_{i}}^{2}\geq x_{n}\sum_{i=1}^{n-1}x_i\] for all real numbers \(x_1,\space x_2, \space x_3,\ldots,\space x_n\).

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