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Math Help - Help with another limit

  1. #1
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    Help with another limit

    I am completley stuck on this limit and have no clue what to do here, I am trying to use the ratio test to see if it converges or diverges. The limit as k goes to infinity of (k!4^k)/((k+1)!4^(k+1)). Can anybody help me figure out what to do here?

    Thank You
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  2. #2
    Moo
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    Hello,

    (n+1)!=1*2* \dots *n*(n+1)

    n!=1*2* \dots *n

    So (n+1)!=(n+1)*n!

    -> How can you simplify \frac{k!}{(k+1)!} ?

    Then 4^{k+1}=4^k*4^1=4^k *4

    So how can you simplify \frac{4^k}{4^{k+1}} ?
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