# Series and Limits Problem

1. Mar 29, 2016

### Ethan Godden

1. The problem statement, all variables and given/known data
I am supposed to determine whether the summation attached is convergent or divergent

2. Relevant equations
Alternating Series Test
Test for Divergence

3. The attempt at a solution
The attempted solution is attached. Using the two different tests I am getting two different answers.

#### Attached Files:

• ###### Problem.pdf
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168.9 KB
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41
2. Mar 29, 2016

### LCKurtz

It is much preferred for you to type the problems rather than post a download.

You have $\frac 1 {\sqrt{n+1}}\to 0$ which is correct. Now since$$0 \le \left | \frac {(-1)^n} {\sqrt{n+1}}\right | \le \frac 1 {\sqrt{n+1}}$$ how could the alternating one not go to zero? And, by the way, $(-1)^\infty$ makes no sense.

Last edited: Mar 29, 2016
3. Mar 29, 2016

### Ethan Godden

Okay, you used the squeeze theorem which makes sense, but why doesn't the test for divergence work? Isn't (-1) undefined meaning the limit is undefined meaning the series is divergent?

4. Mar 29, 2016

### LCKurtz

Yes, as I said, $(-1)^\infty$ makes no sense or, as you say, is undefined. What is happening in this problem is that the denominator is getting larger and the numerator is either plus or minus 1 for any n. The fraction gets small no matter the sign, so regardless of the alternating sign the fraction goes to zero.