Question $6$: The exponential function can be calculated or approximated using the given Taylor

series $($function to determine infinite sum$)$:

where n$!$ is the factorial of n$.$ The greater the value of n$,$ better the approximation.

$$ Write a MATLAB program in script, a $.$m file to determine e

$2$

$.$ Using a for loop for the

algorithm representing the above Taylor series with x $=2$ and n $=0$ to $30.$ Use built$-$in

MATLAB function, factorial$($n$)$ for n$!$

$$ Also include in your program the verification of the Taylor series program using MATLAB

built$-$in function, exp$(2)$ and also display the result. When running your program, only these

two results should be displayed.