# Problem 190: Maximising a weighted product

![graphic](img190.gif)

Let Sm = (x1, x2, ... , xm) be the m-tuple of positive real numbers with
x1 + x2 + ... + xm = m for which Pm = x1 \* x22 \* ... \* xmm is
maximised. For example, it can be verified that \[P10\] = 4112 (\[ \] is
the integer part function). Find Σ\[Pm\] for 2 ≤ m ≤ 15.