Geometric Series Test Rather Than Integral Test

[Bashyboy]

Homework Statement

$\sum_{n=1}^{\infty} \frac{1}{2^n}$

Homework Equations

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?

 

[HallsofIvy]

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

 

[SammyS]

Homework Statement

$\sum_{n=1}^{\infty} \frac{1}{2^n}$

Homework Equations

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?

Hint:

No manipulation is required.

 

[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?

 

[SammyS]

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

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.