# Ratio test problem

1. May 7, 2014

### Dobie

1. The problem statement, all variables and given/known data

See attached image. (it should say "ratio" not "ration")

2. Relevant equations

Ratio series test: An+1/An

3. The attempt at a solution

I have worked this problem over and over and continue to get the same solution. Some guy worked it on the board a couple of days ago and got something different, which our teacher said was right.

I cannot reproduce this and I wonder if the student got it wrong and the professor just didn't check it very well. Either that or I'm losing my mind. There is a test tonight and the problem is from a review Monday.

The answer I continue to get is: 1/2n^2+2n = 1/∞ = 0<1 so it converges.

The other student got: 2n+1/n+1 = 2>1 diverges.

I can post a picture of my work if needed. If I really do have the incorrect answer, can someone please post an image of their work so that I can see whats going on?

Thank you

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Last edited: May 7, 2014
2. May 7, 2014

3. May 7, 2014

### Dobie

Well thanks for the advice on using parentheses. I do not believe the formula should have them as you have in your correction, though.

Was the other student's answer correct? Did you solve the problem or just assume I missed it based on my sloppy use of (or lack thereof) parentheses?

My work:

Edit: went back and did not distribute the 2.

Last edited: May 7, 2014
4. May 7, 2014

### LCKurtz

Yes.

It's hard to follow what you did but I think you have calculated$$(2(n+1))! = (2n+2)n!$$which isn't correct.

5. May 7, 2014

### Dobie

Even if I do not distribute the 2 (I pulled the 2 back out toward the end), I am still left with 1/∞. Thanks for illustrating the correct way to solve the problem, though!

6. May 7, 2014

### xiavatar

$(2(n+1))!=(2n+2)(2n+1)((2n)!)$

7. May 7, 2014

### Dobie

Thank you so much for this explanation. I did not know it expanded like that in this case, but I've reworked it and it comes out perfectly.

8. May 7, 2014

### xiavatar

Just note that for next time that (a(n+1))!=(an+a)!=(an+a)(an+a-1)(an+a-2)...(2)(1). Always remember to carry out the operation in the parentheses before you do the operations outside of the parentheses. I'm guessing that's why you factored out a 2. You cannot fact out the 2 like that when your doing a factorial.

Examples.
(2*3)!=(6)!=6*5*4*3*2*1.
(4*3)!=(12)!=12*11*10*...*3*2*1