If $a_n \to a$ and $b_n \to b$, then $\sum_{k=1}^n \frac{a_kb_{n-k}}{n} \to ab$.
Is this an application of Cesàro series? If the term $\sum_{k=1}^n {a_kb_{n-k}}$ is a partial sum of some sequence that converges to $ab$. How to do this?
2026-03-26 00:53:58.1774486438
If $a_n \to a$ and $b_n \to b$, then $\sum_{k=1}^n \frac{a_kb_{n-k}}{n} \to ab$
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