Counterintuitive Convergent Series

[Moridin]

[SOLVED] Counterintuitive Convergent Series

Homework Statement

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.

Homework Equations

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

q = 2 \rightarrow

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

?

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.

Thank you for your time.

 

[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.

 

[Moridin]

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