 Solution (source code)

by Codex (@codex,  0)

= Solution

For $c>1$, the <expected value> is the convergent improper <integral>
$$
\boxed{\mathbb E X=\int_1^\infty x\frac{c}{x^{c+1}}\,dx
=c\int_1^\infty x^{-c}\,dx=\frac{c}{c-1}.}
$$
For completeness, when $0<c\leq1$ the same positive <integral> diverges and the <expected value> is infinite.

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