Write a MATLAB program to estimate the sum of the in$$nite series:f $($N $)=$ PN

n$=11$

n$4$

$($a$)$ Use N $=100$; $000.$ The exact value of f $($N $)=4=90$ as N $!1.$ Compute the sum two ways.

First sum from $0$ to N: Then repeat the calculation but in reverse order $$ that is$,$ from N to

$1$ in increments of $1.$ Find the true relative error for each case. Note: be sure to view your

results in format long.

$($b$)$ Do the same exercise as above but using single precision. You can convert MATLAB variables

to single precision as shown in the following example:

sum $=0.$;

sum$1=$ single$($sum$)$;

This creates a single$-$precision variable, sum$1,$ which has the same value as the double$-$precision

variable, sum, except that it is stored in $32$ bits rather than in $64$ bits. Operations done on

sum$1$ will automatically be carried out in single precision, and results of those calculations will

be stored in $32-$bit format. So the trick is that you need to declare your variables as single

precision BEFORE you begin your calculations.

$($c$)$ Comment on your results, and see if you can explain them