This homework requires understanding of example $1$

Consider the power series for the hyperbolic cosine, $cosh(z)$

$cosh(z)={\displaystyle \underset{k=0}{\overset{}{}}}\frac{z^{2k}}{(2k)!}=1+\frac{1}{2!}{z}^2+\frac{1}{4!}{z}^4+\frac{1}{6!}{z}^6+$cdots,

valid for

Working as in example $1,$ modify EX$1.$m and prepare a new script that provides an approximation to $cosh(z)$ by summing the first $n$ terms of the series, plots the $k^{th}-$order approximation vs $k$ and stores the values in a text file. Calculation of as $[$:$z^{2^{**}k}\}$ and of factorials using the factorial$()$ function or a for$-$end statement is not allowed. The calculation should be done by considering the ratio $\frac{b_k}{b_{k-1}}$ as in example $1$ and should be using minimum arithmetic operations. Note that $b_k=\frac{z^{2k}}{(2k)!}.$

Test the script file for $z=+-3$ and for several values of $n$ and make sure it produces correct results prior to uploading to canvas.

Hint regarding factorials:

$n1*2*3$cdotsn

$(n+1)1*2*3$cdotsn$*(n+1)$

Thus $(n+1)n!*(n+1).$

Example $1$ is shown below