Let’s have some fun with divergent geometric series. It can be shown (or rather, argued) that

In fact, Euler already knew this. Intuitively one can simply try the well-known closed form for geometric series, that is

for (at your own risk!), to find the solution:

Alternatively, you can use Riemann’s Zeta function

which, with , results after heavy rewriting in again.

For a different perspective, see Bill Gosper in HAKMEM 154, where he figures:

By this strategy, consider the universe, or, more precisely, algebra:

let

now add X to itself;

thus, so

therefore algebra is run on a machine (the universe) which is twos-complement.