One cool application of infinite series is to generate exact formulas for $.$ Here are two such formulas

The arctan formula $($found by evaluating the Maclaurin series for $arctan(x)$ at $\frac{}{4}$ :

$=4{\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{2n+1}$

Ramanujan's formula:

$\frac{1}{}=\frac{2\sqrt[\phantom{2}]{2}}{9801}{\displaystyle \underset{k=0}{\overset{}{}}}\frac{(4k)!(1103+26390k)}{(k!{)}^4{396}^{4k}}$

approximation to $.$

Print the results to the screen, and compare with the actual value of $.$

Need more practice with this? Here are some free resources:

Matlab Onramp, do section $13\mathrm{.}1,13\mathrm{.}2,$ and $13\mathrm{.}3.$ https$//$hww mathworks com$/$learn$/$tutorials$/$matlab$-$onramp. html

TutorialsPoint: https$//$www

tutorialspoint.com$/$matlab$/$matlab$\_$loops. htm

Office hours $-$ you're always welcome.