Here's a lesson that uses the for-loop to study a series (a series is a bunch of numbers added together). In pre-calculus or calculus, you might have
learned that $\Sigma\frac{1}{n}$ diverges (or gives an infinite value if you run the sum over an infinite
number of terms). If you take the first few terms in the sum, you'll get $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...$. Each term
gets smaller and smaller, so does it really diverge? Let's write some code here to test it.

As you work on this, notice the similarities between the $\Sigma$ from math, and the `for-loop`

in programming.
In this case $\Sigma_{n=a}^{b}$ runs $n$ from $a$ to $b$, while `for n=a,b do`

runs `n`

from `a`

to `b`

.

`sum=sum+`

line to see if $\Sigma\frac{1}{n}$ diverges.
Type your code here:

See your results here:

Fix the for-loop to run

`n`

over as many terms as you'd like. Start with 50 or 100. Then fix the `sum=sum+`

line
to add $1/n$ to the sum, with each iteraction of the for-loop.
When done, see if:

- $\Sigma\frac{1}{n^2}$ converges or diverges.
- How about $\Sigma\frac{(-1)^{n-1}}{n}$?

Does your code work? Want to run it on your iPhone?

Here's your code:

- Use [Control]-[C] (Windows) or [⌘]-[C] (MacOS) to copy your code.
- Paste it using [Control]-[V] (Windows) or [⌘]-[V] (MacOS) into
this page
- Then click the "Use on iPhone" button that you'll see.