$\begin{align}
&S_1=\displaystyle\sum\limits_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n}\ln n}}{n!}}
\\\\
&S_2=\displaystyle\sum\limits_{n=1}^{\infty }{\frac{{\ln n}}{n!}}
\end{align}$
**Which series converges?**
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**Based on your answer, what can we say about $S_1$?**
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