What Verizon Got when They Pissed off a Customer!

[Airstream_Bill]

I thought that this was unique, so I am posting the picture.

[jtmulc]

For anyone not aware, Randall Patrick Munroe is the creator of XKCD. You've seen his work online.

[calguyhunk]

For anyone not aware, Randall Patrick Munroe is the creator of XKCD. You've seen his work online.

I was just about to Google. :P Thanks. Here's his Wiki BTW. I wonder what made him so pi$$ed at Verizon anyways. Maybe an inflated bill? :dunno:

The entire background story as reported by Boing Boing.

I thought that this was unique, so I am posting the picture.

Thanks for posting this, Bill. Comedy gold for us Math loving nerdy types :lol:

Having said that though, even though my Calculus is a tad rusty through years of disuse, I somehow don't think the Math is right. ;)

The infinite sum is a geometric series of the form E a* r^k, with a=1, r= 1/2, and with k starting at 1 and not 0, since a^0 = 1.

(k=0 approaching ∞) E a*r^k = a / (1-r)

For a=1 and r=1/2, the sum is 2.

So, (k=1 approaching ∞) E 1/(2^k) = 1, as explained above.

Euler's identity states that e^(i*pi) + 1 = 0, or e^(i*pi) = -1.

Euler's formula states that e^(i*x) = cos(x) + i*sin(x).

For the special case x=pi, this becomes:

e^(i*pi) = cos(pi) + i*sin(pi)

e^(i*pi) = -1 + i*0

e^(i*pi) = -1

If x=0, we have e^(i*0) = e^0, so we expect the answer to be 1 through the formula, and this is indeed the case:

e^(i*0) = cos(0) + i*sin(0)

e^(i*0) = 1 + i*0

e^(i*0) = 1

As for the infinite summation of 1/(2^n), this is equivalent to 1. This could be expressed as a limit, but not necessary, since the upper limit is infinity (n->∞) and not from n=1 to N, in which case it would have been appropriate to express it as the limit.

The summation looks like this in simple terms:

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...

As you add each term, the summation approaches 1:

0.5, 0.75, 0.875, ...

After 4 terms: 0.938

**************************

After 24 terms: 0.99999994

***************************************

After an infinite number of terms: 0.99999999... with an infinite number of nines being equivalent to 1.

Since e^(i*pi) + the summation = -1 + 1 = 0, the amount payable is $0.002.

The guy who made the meme (presumably the one who also worked the math out) made an error by writing 2*pi rather than i*pi, resulting in the $536 dollar end result. ;)

EDIT - Yippie!!! I've found other websites where posters agree with me. Site 1 and Site 2. :D This seems like a really old meme from 2006! Here's the original blog post straight from the horse's mouth. I seem to have missed the entire episode completely. Must have been too busy with my studies. :P

Edited June 10, 2014 by calguyhunk