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\(\lim _{n \rightarrow \infty} \frac{n !}{(n+1) !-n !}=\)
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\(\begin{gathered}
\operatorname{Lim}_{n \rightarrow \infty} \frac{n !}{(n+1) !-n !}=\operatorname{Lim}_{n \rightarrow \infty} \frac{1}{(n+1)-1} \\
=\operatorname{Lim}_{n \rightarrow \infty} \frac{1}{n}=0
\end{gathered}\)
\operatorname{Lim}_{n \rightarrow \infty} \frac{n !}{(n+1) !-n !}=\operatorname{Lim}_{n \rightarrow \infty} \frac{1}{(n+1)-1} \\
=\operatorname{Lim}_{n \rightarrow \infty} \frac{1}{n}=0
\end{gathered}\)
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