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Math Help - Recursive definition??

  1. #1
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    Recursive definition??

    I'm really sorry about how messy this looks; I'm still trying to figure out how to use the math notation thing.

    Anyway, the problem is:

    Given A0=1 and An+1=(3*An)+1, find the definition for An

    I just have no idea how to go about doing this. You don't have to give the answer, just any sort of hint as to procedure would be great. Thank you!
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  2. #2
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    Quote Originally Posted by sfitz View Post
    I'm really sorry about how messy this looks; I'm still trying to figure out how to use the math notation thing.

    Anyway, the problem is:

    Given A0=1 and An+1=(3*An)+1, find the definition for An

    I just have no idea how to go about doing this. You don't have to give the answer, just any sort of hint as to procedure would be great. Thank you!
    A_0=1

    A_1=3 A_0+1=3+1

    A_2=3 A_1+1=3^3 + 3 +1

    A_3=3 A_2+1=3^3+3^2+3+1

    and so on..

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    A_0=1

    A_1=3 A_0+1=3+1

    A_2=3 A_1+1=3^3 + 3 +1

    A_3=3 A_2+1=3^3+3^2+3+1
    So I think I'm getting An=Sum from i=1 to n of 3^i

    That makes sense, because you multiply each previous term by 3, so there must be an exponent in there... haha, i think it's coming together in my head. Thank you!
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  4. #4
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    Quote Originally Posted by sfitz View Post
    So I think I'm getting An=Sum from i=1 to n of 3^i Mr F says: No.

    That makes sense, because you multiply each previous term by 3, so there must be an exponent in there... haha, i think it's coming together in my head. Thank you!
    Close. But actually the sum will be from i = 0: A_n = \sum_{i = 0}^n 3^i.
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