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Math Help - Ratio Test for Convergence

  1. #1
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    Ratio Test for Convergence

    Use the Ratio Test to determine whether converges or diverges.

    (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For ,


    (b) Evaluate the limit in the previous part. Enter as infinity and as -infinity. If the limit does not exist, enter DNE.
    =

    (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose Converges Diverges Inconclusive

    So out of all my work all of this is correct except the denominator. I tried everything. When I put in (2n+2)! my online assignment says cancel out further and to simplify. WHAT???

    I hate convergence/divergence. You all will soon learn that from my next several posts haha

    Thank you to anyone that can help!
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  2. #2
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    Re: Ratio Test for Convergence

    you better have a look here first and then show us some of your work...

    Ratio test - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Ratio Test for Convergence

    This looks fairly straightforward to me but it is impossible to suggest where you might have made a mistake without seeing what you did! You know, of course, that a_n= \frac{9^n}{(2n)!}. So what is a_{n+1}? What is \frac{a_{n+1}}{a_n}? What can you cancel?
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  4. #4
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    Re: Ratio Test for Convergence

    Quote Originally Posted by cld1126 View Post
    So out of all my work all of this is correct except the denominator. I tried everything. When I put in (2n+2)! my online assignment says cancel out further and to simplify. WHAT???
    OK, so here's something that can actually be addressed. The more working out you show us, the more guidance we are able to give you.

    Notice that (2n + 2)! = (2n + 2)(2n + 1)(2n)!

    Can you see how the (2n)! will cancel?
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    Re: Ratio Test for Convergence

    Quote Originally Posted by Prove It View Post
    OK, so here's something that can actually be addressed. The more working out you show us, the more guidance we are able to give you.

    Notice that (2n + 2)! = (2n + 2)(2n + 1)(2n)!

    Can you see how the (2n)! will cancel?
    Thank you so much, yes that makes perfect sense now. I was using the factorial incorrectly. My textbook gives a lot of proofs with almost no application or examples. The answer they were looking for was (2n+2)(2n+1). Thank you again.
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