Well, I can't see how to do this. But I will offer this useless tidbit of mathematical (non)information:
In the 2-adic norm, the infinite series 1+2+4+8+16+... converges to -1 (as the formula for infinite geometric series would "predict"). So 2+4+8+16+... converges to -2.
It's a bit like what you get on a computer
(which uses 2's complement
, if you're into that kind of thing
). Take 1, then repeatedly shift left
(this is integer arithmetic
we're doing here!). After a finite
number of steps (usually 32
nowadays), you're just adding
, so you might as well declare the series has converged on your computer. Guess what? The result is (binary
, which is precisely -1.
This is not a coincidence.
Mathematical garbage disposed of in an environmentally hazardous manner by the E2WDC -- "Our business is garbage!".