# Homework Help: Geometric Series Test Rather Than Integral Test

1. Oct 6, 2012

### Bashyboy

1. The problem statement, all variables and given/known data
$\sum_{n=1}^{\infty} \frac{1}{2^n}$

2. Relevant equations

3. The attempt at a solution
Could I some how manipulate this to fit a geometric series, so that I may instead use the geometric series test?

2. Oct 6, 2012

### HallsofIvy

$$\frac{1}{2^n}= \left(\frac{1}{2}\right)^n$$

3. Oct 6, 2012

### SammyS

Staff Emeritus
Hint:

No manipulation is required.

4. Oct 6, 2012

### Bashyboy

Well, I was told by my teacher that n couldn't equal one for the geometric series to be implemented, was he, perhaps, wrong?

5. Oct 6, 2012

### SammyS

Staff Emeritus
Do you mean, n can't start at 1, it must start at zero?

If so factor 1/2 out of your series & change the index accordingly,

else,

Add 1 to your series so that it starts at n=0, and subtract 1 from your result.