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Ratio test did I do it right?

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi
    I want to see if you guys could check my work an tell me if i did it correct and also explain me how to cancel "look at the graph"


    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Nov 10, 2009
  2. jcsd
  3. Nov 9, 2009 #2
    Yes.

    When in doubt, set a term an equal to what is being summed. In this case, an = 2^n/n!.

    Now, get the next term in the series so an+1. In this case, an+1 = 2^(n+1)/(n+1)!.

    Then, plug in an and an+1 into [tex]|\frac{a_{n+1}}{a_{n}}|[/tex]

    Now, the n! cancels because n! is equivalent to n*(n-1)(n-2)(n-3)(n-4). Whereas (n+1)!, is equivalent to (n+1)(n)(n-1)(n-2)(n-3)(n-4).

    So, as you can see, the terms to the right of (n+1) are canceled out.

    Sincerely,

    NastyAccident
     
    Last edited: Nov 9, 2009
  4. Nov 10, 2009 #3

    thanks for the explanation was very helpful
     
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