a$)$ Suppose the following infinite series converges to $e.$

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{(k-1)!}=1+1+\frac{1}{2!}+$dots

Using Matlab, write a for loop to sum the first twenty terms of the series and compute the relative error. Secondly, write a while loop that will determine how many terms must be summed to produce an approximation of $e$ that is correct to $3$ significant figures. Use fprintf to output your results. Lastly, plot a well labelled figure of the infinite series versus its indices. Submit both the code, the figure, and your output.