> 
> Evaluate $\lim\_{n\to\infty}(1+\frac{1}{a\_1})(1+\frac{1}{a\_2})\cdots(1+\frac{1}{a\_n})$,
>  where $a\_1 = 1$, $a\_n = n(1+a\_{n-1})$
> 
> 
> 

\begin{align\*}
&\lim\_{n\to\infty} \left(1+\frac{1}{a\_1}\right)\left(1+\frac{1}{a\_2}\right)\cdots\left(1+\frac{1}{a\_n}\right) \\
&= \lim\_{n\to\infty} \frac{1}{a\_1} \cdot \frac{1}{2} \cdot \frac{1}{3} \cdots \frac{1}{n} \cdot (a\_n + 1) \\
&= \lim\_{n\to\infty} \frac{a\_n + 1}{n!}.
\end{align\*}

Then I'm stuck. How to proceed?