$4$ Calculating $e$

You'll use this series equation to approximate $e.($Trivia: this is the Taylor series for $e^x$ with $x=1.)$

$e={\displaystyle \underset{k=0}{\overset{n-1}{}}}\frac{1}{k!}=1+\frac{1}{1}+\frac{1}{2}+\frac{1}{6}+\frac{1}{24}+\frac{1}{120}+\frac{1}{720}+\frac{1}{5040}+$cdots

When you see a Sigma $({\displaystyle \underset{?}{\overset{?}{}}}),$ think of a for loop. In this case, the for loop starts at $0$ and ends at $n-1.$ Here is one way to do that:Important: The summation $($sum$\_($k$=0)^($n$-1)(1)/($k$!))$ and the for loop run from $0$ to n$-1.$ That's because for a given value of n we want to have n terms in the series.$$ To do: In your copy of nummy $.$ c you'll see a function called my$\_$e$().$ Convert the mathematical series above into C within that function. You'll be using double type variables for everything except the for loop's index, which is an int. Note: You should not write or use a factorial function. Instead you should use a variable to store $($k$-1)!$ and multiply it by k on each loop iteration, essentially using k$!=($k$-1)!$xx k$.$ There will be an example of this in lecture. Also, remember that $0!=1.$ This is in C