Select the FIRST correct reason why the given series converges.

[McAfee]

Homework Statement

Select the FIRST correct reason why the given series converges.

A. Convergent geometric series
B. Convergent p series
C. Comparison (or Limit Comparison) with a geometric or p series
D. Converges by alternating series test

The Attempt at a Solution

I will go over my reasoning for each problem.

1. A. I really it was a geometric and r is 1/16 which is less than 1 meaning it is convergent.

2. I want to say it is comparsion but I'm not sure.

3. Not sure.

4. B. Want to say alternating but it doesn't fit.

5. D. It alternates, ignoring signs it decrease, and the limit as x goes to infinity equals 0. All meaning it converges due to the alternating series test.

6. D. It alternates, ignoring signs it decrease, and the limit as x goes to infinity equals 0. All meaning it converges due to the alternating series test.

 

[McAfee]

If anyone has any ideas. I'm truly stuck on this one problem.

 

[McAfee]

Just to update everyone. After further investigation I was able to figure out all the answers.
Here they are.

1. A. I really it was a geometric and r is 1/16 which is less than 1 meaning it is convergent.

2. B. Rewrite this as (-1)^n * n / (n^9 * (-1)^n) = 1/n^8.

3. C. Use 0 < sin^2(3n) < 1, so that sin^2(3n)/n^2 < 1/n^2

4. D. It alternates, ignoring signs it decrease, and the limit as x goes to infinity equals 0. All meaning it converges due to the alternating series test.

5. D. It alternates, ignoring signs it decrease, and the limit as x goes to infinity equals 0. All meaning it converges due to the alternating series test.

6. D. It alternates, ignoring signs it decrease, and the limit as x goes to infinity equals 0. All meaning it converges due to the alternating series test.