# Sum of a geometric series

1. Apr 23, 2006

### Mathman23

Hi

Can I claim that in order to find the sum of the series:

$$\sum_{n = 0} ^{\infty} 2^{- n}$$

$$\sum_{n = 0} ^{\infty} 2^{- n} = \sum_{n = 0} ^{\infty} x^n = \frac{1}{1-x}$$ ???

Sincerely Yours
Fred

Last edited: Apr 23, 2006
2. Apr 23, 2006

### matt grime

No, you can't claim *that* (since it is false; one side is a number, the other is a power series in x), but you can use the series if you do so legitimately.

3. Apr 23, 2006

### HallsofIvy

Staff Emeritus
In other words, since 2-n= (2-1)n, yes, if x= 2-1. (Assuming, of course, that the sum converges. Can you show that?)