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Math Help - Sum of a Sequence

  1. #1
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    Sum of a Sequence

    Hi, so I have a sequence with a rule in recursive form, and I need to find a simple expression for the sequence that is not recursive, which I am having a hard time doing, even though it feels it shouldn't be giving me as much trouble as it is .

    Find a simple (non-recursive) expression for the sequence;
    a_{1} and a_{n}=2a_{n-1}+1 for n=2,3,4, .....

    I can't seem to find a pattern here that I could write non-recursively, the terms I found are

    a_{1}=1 ,
    a_{2}=3 ,
    a_{3}=7 ,
    a_{4}=15 ,
    a_{5}=31 ,
    a_{6}=63 , ....

    Anyone got any tips about what to look for in this sequence? I'm not sure what I'm missing to not see this one non-recusively. Thanks!
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  2. #2
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    Quote Originally Posted by superduper View Post
    Hi, so I have a sequence with a rule in recursive form, and I need to find a simple expression for the sequence that is not recursive, which I am having a hard time doing, even though it feels it shouldn't be giving me as much trouble as it is .

    Find a simple (non-recursive) expression for the sequence;
    a_{1} and a_{n}=2a_{n-1}+1 for n=2,3,4, .....

    I can't seem to find a pattern here that I could write non-recursively, the terms I found are

    a_{1}=1 ,
    a_{2}=3 ,
    a_{3}=7 ,
    a_{4}=15 ,
    a_{5}=31 ,
    a_{6}=63 , ....

    Anyone got any tips about what to look for in this sequence? I'm not sure what I'm missing to not see this one non-recusively. Thanks!
    adding 1 to every term will make things much clearer.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    adding 1 to every term will make things much clearer.
    a-HA!

    a_{n}=2^n - 1,\ where\ a_{1}=1

    I'm awful slow today, thanks!
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