Counterintuitive Convergent Series

1. Nov 12, 2007

Moridin

[SOLVED] Counterintuitive Convergent Series

1. The problem statement, all variables and given/known data

One of my new textbooks in mathematical analysis makes a very strange claim (not sure if it was a true claim or some random historical anecdote) for a convergent series in one of its short sections on the history of mathematics, which I am baffled about.

2. Relevant equations

$$1 + q + q^2 + q^3 + ... = \frac{1}{1-q}$$

$$q = 2 \rightarrow$$

$$1 + 2 + 4 + 8 +.... = -1$$

?

3. The attempt at a solution

It can either be one of two explanations in my mind; it is either completely false in some way (undefined or misapplication of a theorem or wrong approach) or only applies in the realm of mathematics and you do not get -1 apples if you keep adding them together.

Last edited: Nov 12, 2007
2. Nov 12, 2007

Galileo

I do hope the textbook mentions that not all values of q are permitted for that expression.
The left side converges only when |q|<1.

3. Nov 12, 2007

Moridin

Indeed, I finally managed to find the passage it was referring to. Thanks for your help.