Suppose $$A(m) = \left(1+\frac{1}{m}\right)^m.$$
As discussed in class, $A(m)$ approaches $$e = 2.71828183\ldots$$ as $m$ increases without bounds. This exercise illustrates that fact. You'll need to enter numerical values of $e-A(m)$ that are correct to 4 digits (after the initial zeros). You can compute them with your calculator, and you may find it convenient to use scientific format. Note how the difference of $e$ and $A(m)$ approaches zero, and $A(m)$ approaches $e$ as $m$ grows.
If you are curious you can see the first 10,000 digits of e here.


$e-A(1) =$ .
$e-A(2) =$ .
$e-A(10) =$ .
$e-A(100) =$ .
$e-A(1,000) =$ .
$e-A(10,000) =$ .
$e-A(100,000) =$ .
$e-A(1,000,000) =$ .