# Infinity is -1/12

Proof that 1 + 2 + 3 + 4 ... = -1/12.

Did you know that the sum of all whole numbers is equal to -1/12? In this article we find out how it’s possible and prove it ourselves using simple algebra and math!

*DISCLAIMER: The math used in this article doesn’t count as real reasoning; it’s
just a fun thing to think about. See
this video by Mathologer for more
information.*

## The Series

We will define three series that we need to find out: $S$, $G$, and $H$.

## Solving for G

Our base step is to solve $G$. This is pretty simple:

Now we have proved that $G = \frac{1}{2}$!

## Solving For H

Now that we’ve solved for $G$, we can use it to solve $H$. Here’s the answer for this:

Now we have proved that $H = \frac{1}{4}$!

## Solving For S

Now that we’ve shows what $G$ and $H$ are equal to, it’s time to finally solve for $S$.

Now we have proved that $S = -1/12$, and we’re done!

## Sources & Resources

I originally found out about this phenomenon at this YouTube video by Numberphile. It’s a great video and you should check it out.