# Homework Help: Sequence e^2/2^n, converge or diverge (easy)

1. Feb 5, 2012

### 8point1

1. The problem statement, all variables and given/known data
does the series $e^n/2^n$ converge or diverge?

does the series $2^n/e^n$ converge or diverge?

3. The attempt at a solution

I took $lim→∞ e^x/2^x$ and am getting ∞, so it diverges, right?

I also used L'Hopital's rule and got the same result.

My prof hinted that I was wrong... what am I missing?

Thanks!

Last edited: Feb 5, 2012
2. Feb 5, 2012

### Dick

Yes, you are right. e/2 is greater than 1. The series diverges.

3. Feb 5, 2012

### 8point1

what about 2/e?

4. Feb 5, 2012

### Dick

You tell me. What do you know about the geometric series r^n?

5. Feb 5, 2012

### checkitagain

8point1,

there is a distinction. Those expressions are the general terms
of the sequences and the series.

The summations of those terms are the respective series.

6. Feb 5, 2012

### 8point1

The sequence diverges, so the series must diverge also, correct?

7. Feb 5, 2012

### Dick

That's correct for (e/2)^n. (2/e)^n is different.

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