\item (20 pts)
Find the smallest $N$ so that
$
\displaystyle{ \left| \sum_{i=0}^N {3^i \over i!} - e^3 \right| <10^{-5} }.
$
Let your code print the answer $N$ and 
$
\displaystyle{ \left| \sum_{i=0}^N {3^i \over i!} - e^3 \right| }
$
on screen,
and also write them down on the answer sheet.
Extra credits for more efficient method(s).