# Converge or not

1. Jun 5, 2009

### asset101

Does the series $$\sum\frac{2}{2^{n}}$$

converge??

(Note that bounds on the running index n are from 1 to infinity)

I have tried ratio test but it returned a value of 1 (showing nothing).

I can see from the table function on my calulator that the term eventually diminsh to (not including zero).

Any help would be appreciated.

2. Jun 5, 2009

### HallsofIvy

Staff Emeritus
Can you show how you did the ratio test? The ratio is NOT 1.

3. Jun 5, 2009

### AUMathTutor

Rememer, you can pull anything not involving an "n" out of the summation. So the 2 in the numerator can come out. Then you have

2 (SUM) 1/2^n

This can also be written as

2 (SUM) (1/2)^n

You should be able to recognize the SUM as a notable one, and use the rules pertaining to that kind of summation to determine whether or not it converges. And if it converges, does multiplying by 2 change any of that?

4. Jun 5, 2009

### asset101

Sorry fellas the question should read

Does the series $$\sum\frac{n}{2^{n}}$$

converge??

(Note that bounds on the running index n are from 1 to infinity)

I have tried ratio test but it returned a value of 1 (showing nothing).

I can see from the table function on my calulator that the term eventually diminsh to (not including) zero.

Any help would be appreciated

5. Jun 5, 2009

### Dick

Ratio test should still not give you a value of 1. Can you show how you got that?

6. Jun 5, 2009

### nicksauce

What comes to my mind would be doing a comparison test with the integral of x*exp(-x).

7. Jun 6, 2009

### Staff: Mentor

What Dick said. The ratio test is definitely the test to use. If you got a limit of 1, you're doing something wrong.