Consider the following series where $=[1,...,]$ is an input vector of $$ points.

$=()$

$$

$=1$

a$)$ Write a numerical solver for the series using a for$-$loop. Test the code for $()=1$

$22$ when $$

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

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

$\backslash$infty $.$ 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$).$