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Math Help - help with infinite sum

  1. #1
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    help with infinite sum

    i'm trying to do some calc hw, but i ran into this equation

    Σ t^k = 5
    k=0

    is there some kind of rule which changes this equation so i can solve for k?
    Last edited by ThePerfectHacker; January 23rd 2006 at 03:14 PM.
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  2. #2
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    Quote Originally Posted by hongster5
    i'm trying to do some calc hw, but i ran into this equation

    Σ t^k = 5
    k=0

    is there some kind of rule which changes this equation so i can solve for k?
    Solve for k?!? That makes no sense you probably mean for t

    This is,
    1+t+t^2+t^3+...=5

    Assuming that this infinite series converges then it is a geometric series for |t|<1 and such as its sum is 5. But its sum is given by \frac{1}{1-t}.
    Thus,
    \frac{1}{1-t}=5
    thus, t=\frac{4}{5}
    Q.E.D.

    Something interesting to note,
    the eqaution
    \frac{1}{1-t}=r
    Always has a unique solution,
    namely,
    \frac{r-1}{r}
    and that,
    |\frac{r-1}{r}|<1
    Thus, any infinite geometric sum can be made to converge to any real number.
    Last edited by ThePerfectHacker; January 23rd 2006 at 03:03 PM.
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  3. #3
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    thx alot. i wasnt thinking of geometric sequences... not that i would have known that equation anyways, lol
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  4. #4
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    Welcome
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