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Math Help - finding the values of constant c.....

  1. #1
    ixi
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    finding the values of constant c.....

    For what values of the constant c do the following define mas functions on the positive integers: x = 1,2,...?

    f(x) = c2^(-x) / x

    can someone point me the right direction? I don't know where to get started


    thanks
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  2. #2
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    \sum\limits_{k = 1}^\infty  {\frac{1}<br />
{{k \cdot 2^{^k } }}}  = ?
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  3. #3
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    So you know the sum of the probability mass function has to equal one. This is the definition of a pmf. So set up the sum as Plato pointed out, set it equal to one, and solve for c.
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  4. #4
    ixi
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    i did some easier pmf problems in my text, where x goes from 1 to 4 and that's easy to solve for c.

    but for this problem....

    1/2c + 1/8c +1/24c +....... = 1
    but what value is it when it goes to infinity?
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    Quote Originally Posted by ixi View Post
    i did some easier pmf problems in my text, where x goes from 1 to 4 and that's easy to solve for c.
    but for this problem.... 1/2c + 1/8c +1/24c +....... = 1
    but what value is it when it goes to infinity?
    Did you see my first post?
    \sum\limits_{k = 1}^\infty  {\frac{1}{{k \cdot 2^{^k } }}}  = \ln (2)
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  6. #6
    ixi
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    but where did the ln(2) come from?
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    Quote Originally Posted by ixi View Post
    but where did the ln(2) come from?
    For folks working these sorts of problems that is a well known sum.
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  8. #8
    ixi
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    Quote Originally Posted by Plato View Post
    For folks working these sorts of problems that is a well known sum.
    Oh i see.

    There are 2 other parts to this question that are similar. Is there a table or site you could direct me to that would have these sums?
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