What is a circle in the 101th dimension?

Algebra Level 5

Given that the numbers are all positive reals x12+x22++x1012=1x_1^2+x_2^2+\cdots+x_{101}^2=1

Maximize n=21011729x1xn \displaystyle \sum_{n=2}^{101} 1729x_1 x_n .

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