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Math Help - factorial in ratio test

  1. #1
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    factorial in ratio test

    Hello all,

    How would you deal with a factorial in a ratio test to find the lim n→∞ .

    here is the question:


    1 / (2n+1)!
    0

    Un = 1 / (2n+1)!
    Un+1 = 1 / (2n+3)!

    (Un)/(Un+1)= 1 / (2n+3)! . (2n+1)! / 1

    (Un)/(Un+1)= (2n+1)! / (2n+3)!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dadon View Post
    Hello all,

    How would you deal with a factorial in a ratio test to find the lim n→∞ .

    here is the question:


    1 / (2n+1)!
    0

    Un = 1 / (2n+1)!
    Un+1 = 1 / (2n+3)!

    (Un)/(Un+1)= 1 / (2n+3)! . (2n+1)! / 1

    (Un)/(Un+1)= (2n+1)! / (2n+3)!
    note that (2n + 3)! = (2n + 3)(2n + 2)(2n + 1)!

    so (2n+1)! / (2n+3)! = (2n + 1)! / (2n + 3)(2n + 2)(2n + 1)! the (2n + 1)!'s cancel leaving 1/(2n + 1)(2n + 2), this goes to zero as n goes to infinity
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  3. #3
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    Thank you!

    What does the infinity on top of the sum sign and the zero below the sum sign mean? As I have seen some questions with n=1 instead of the zero? Thanks


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  4. #4
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    Quote Originally Posted by dadon View Post
    Thank you!

    What does the infinity on top of the sum sign and the zero below the sum sign mean? As I have seen some questions with n=1 instead of the zero? Thanks


    0
    The infinity on top means it is an infinite sum, that is the limit.
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