Form a Matlab program which calculates the ${\displaystyle \underset{?}{\overset{?}{}}}S(n)={\displaystyle \underset{k=1}{\overset{n}{}}}\frac{1}{k^2}$ when $n$ is given as input. Solve the

problem both

$($i$)$ using for$-$loop and

$($ii$)$ without loops using vectorizing. Note that if $x$ is a vector, then the command ${\displaystyle \underset{?}{\overset{?}{}}}(x)$ calculates the

sum of its components.

$($iii$)$ Calculate $S(100)$ using you both programs and give your solution such that the numeric format is

"long".