= Solution
With fixed positive prior parameters and $m_i\ge1$, total exposure satisfies $M=\sum_{i=1}^k m_i\ge k$. Hence $M\to\infty$ as the number of observed years grows, and
$$
\boxed{Z=\frac{M}{M+\alpha+\beta}\longrightarrow1.}
$$
Thus the <credibility estimate> places asymptotically all its weight on the observed policy-weighted claim frequency. The assertion concerns the credibility weight; the scale of the predicted number of claims still includes the known next-year exposure $m_{k+1}$.
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