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.