If $\sum_{i=1}^n x_i = X$, where $X$ is a positive constant and $\forall i, x_i$ is a positive integer, then what is the upper bound of $\sum_{i=1}^{n-1} (x_i x_{i+1})$?
Intuitively, set $ x_1=\dots=x_n=\frac {X}{n}$, and then we obtain the maximum?
2026-04-03 00:22:54.1775175774
Upper bound for the sum of the multiplication of adjacent items of a list
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