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Math Help - Find terms of a sequence and a formula

  1. #1
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    Find terms of a sequence and a formula

    Let {a_n}=(1*3*5*...[(2n+1)/(2n!)]. Find the first five terms of this sequence and a simple formula for the ratio [a_(n+1)]/(a_n)]

    I found the first five terms to be {a_1}=3/2, {a_2}=5/4, {a_3}=7/12, {a_4}=9/48, and {a_5}=11/140. Is this what I was supposed to do?
    I know have to find a formula based on [a_(n+1)]/(a_n)]. How would I do that if a formula was already written, that being [(2n+1)/(2n!)].
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by summerset353 View Post
    Let {a_n}=(1*3*5*...[(2n+1)/(2n!)]. Find the first five terms of this sequence and a simple formula for the ratio [a_(n+1)]/(a_n)]

    I found the first five terms to be {a_1}=3/2, {a_2}=5/4, {a_3}=7/12, {a_4}=9/48, and {a_5}=11/140. Is this what I was supposed to do?
    I know have to find a formula based on [a_(n+1)]/(a_n)]. How would I do that if a formula was already written, that being [(2n+1)/(2n!)].
    Clearly \frac{a_{n+1}}{a_n}=\frac{1\cdot3\cdots(2n+1)\cdot  (2n+3)}{(2n+2)!}\cdot\frac{(2n)!}{1\cdot3\cdots(2n  +1)}=\frac{2n+3}{(2n+2)(2n+1)}
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  3. #3
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    What about the first five terms? Did I find them the right way?
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