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Math Help - Summations help!

  1. #1
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    Summations help!

    Hello,
    I am trying to solve a summation but i keep getting the wrong answer:

    summation of 2^i from i=0 to i=h/2

    I have tried using the geometric series equation and have gotten2^((h/2)+1) - 1) / (2-1) which simplifies to 2^((h/2)+1) - 1 but I don't know how to simplify it from there, assuming it is correct. The answer is said to be: 2^(h+1) - 1. Any help would be very much appreciated. Thank you!
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  2. #2
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    Quote Originally Posted by collegestudent321 View Post
    I am trying to solve a summation but i keep getting the wrong answer:
    summation of 2^i from i=0 to i=h/2
    In what context does the sum occur?
    We usually have indices that are integers, \frac{h}{2} may not be an integer.
    If this is a counting question, your sum may be like this: \displaystyle <br />
\sum\limits_{k = 1}^{\left\lfloor {\frac{h}{2}} \right\rfloor } {2^{ k} } .
    We use the floor function to get an integral index.
    Please clarify this question.
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  3. #3
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    Basically, the summation goes like this:

    1 + 2 + 2^2 + 2^3 + ... + 2^(h/2)

    I do believe h/2 is an integer because h represents the height of a binary search tree. I just can't remember how to work with these summations.

    According to the answer, the geometric series equation is used and is as follows: (1 - 2^((2/h)+1)) / (1-2)
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  4. #4
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    Quote Originally Posted by collegestudent321 View Post
    Basically, the summation goes like this: 1 + 2 + 2^2 + 2^3 + ... + 2^(h/2)
    h represents the height of a binary search tree. I just can't remember how to work with these summations.
    In the future, please give the context of the question.

    In general, \displaystyle\sum\limits_{k = 1}^J {2^k }  = 2^{J + 1}  - 2.
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