Math Help - Convergence by What Test?

1. Convergence by What Test?

Select the FIRST correct reason on the list why the given series converges.

? A B C D E 1.
? A B C D E 2.
? A B C D E 3.
? A B C D E 4.
? A B C D E 5.
? A B C D E 6.

A. Geometric series.
B. Integral test.
C. Comparison with a convergent p series.
D. Ratio test.
E. Alternating series test.

Not a clue once again.

2. Re: Convergence by What Test?

Then you should take a class in "Calculus"! Do you know what the "ratio test", "integral test", etc. are? Have you tried applying those tests to the series?

3. Re: Convergence by What Test?

Originally Posted by HallsofIvy
Then you should take a class in "Calculus"! Do you know what the "ratio test", "integral test", etc. are? Have you tried applying those tests to the series?
Okay, first off I have taken Calculus, and I am in Calculus II right now. My book does not explain these tests very well because it only shows proofs. The examples in the book do not help because they are very simple examples, nothing quite this in depth. Also, my book does not explain answer C or E. The question also asks which comes first, so I imagine that means that some of these can have several tests done to them, but as to why one would be the answer over, if both tests tell you the same thing, that I do not understand.

4. Re: Convergence by What Test?

Originally Posted by cld1126
Okay, first off I have taken Calculus, and I am in Calculus II right now. My book does not explain these tests very well because it only shows proofs. The examples in the book do not help because they are very simple examples, nothing quite this in depth. Also, my book does not explain answer C or E. The question also asks which comes first, so I imagine that means that some of these can have several tests done to them, but as to why one would be the answer over, if both tests tell you the same thing, that I do not understand.
Well we are not prepared to give you a tutorial. It is our stated purpose to help with what you don't understand.
But if you don't know what the alternating series test is then you are asking to be tutored.

Now can you explain why $\left| {\frac{{{{( - 1)}^n}\ln ({e^n})}}{{{n^9}\cos \left( {n\pi } \right)}}} \right| = \frac{1}{{{n^8}}}~?$

If not, I suggest that you lack the necessary background to do this material.
You need to get a live tutor.

5. Re: Convergence by What Test?

Originally Posted by cld1126
Okay, first off I have taken Calculus, and I am in Calculus II right now. My book does not explain these tests very well because it only shows proofs. The examples in the book do not help because they are very simple examples, nothing quite this in depth. Also, my book does not explain answer C or E. The question also asks which comes first, so I imagine that means that some of these can have several tests done to them, but as to why one would be the answer over, if both tests tell you the same thing, that I do not understand.
You should be able to Google any of these to get explanations and/or examples. I suggest that you do this and come back with questions about the methods you do not understand.

-Dan