Problem $5$: Developing a Numerical Solver for a Series

Consider the following series where $x=[x_1,$dots,$x_n]$ is an input vector of $n$ points.

$s={\displaystyle \underset{k=1}{\overset{n}{}}}f(x_k)$

a$)$ Write a numerical solver for the series using a for$-$loop. Test the code for $f(x)=\frac{1}{2}{x}^2$ when $x$

is a vector of evenly spaced points in $0,15$ with step size $h=1.$

b$)$ Due to computational expense, using a for$-$loop can be inefficient and time consuming as $n$

$.$ Write a numerical solver for the series without using a for$-$loop. Test the code for the same

function, interval, and step size in part $($a$).$