Let $\mathcal A$ be a unital complex $*$-algebra, and let $\varphi:\mathcal A\to\mathbb C$ be a state, meaning that $\varphi$ is complex-linear, $\varphi(1_{\mathcal A})=1$, and $\varphi(b^*b)\geq 0$ for every $b\in\mathcal A$. Let $a\in\mathcal A$ be self-adjoint, so $a^*=a$. For each integer $n\geq 0$, define
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\begin{align*}
m_n:=\varphi(a^n).
\end{align*}
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Then for every integer $N\geq 0$ and every $c_0,\dots,c_N\in\mathbb C$,