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Math Help - Help finding closed form of sum

  1. #1
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    Help finding closed form of sum

    Hello all. Can somebody please help with the intermediate steps here? I have reached the point given, but not sure how to advance to the final solution. Many thanks

    \sum_{i=0}^9 (1/2z)^{n}=\frac{1-(2z)^{-10}}{1-(2z)^{-1}}
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  2. #2
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    Krizalid's Avatar
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    that's all, that's a closed form.

    don't know what you want to do further.
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  3. #3
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    Sorry, I wanted to know the necessary steps I need to take to get it into the closed form, the first equation is where I got to, I have the solution but don't know how to get there :-)
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  4. #4
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    ah okay then, can you prove that \sum_{j=0}^n a^j=\frac{a^{n+1}-1}{a-1} ?

    if you can do that, then you're done. (This is a fact known as geometric sum.)
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  5. #5
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    Many thanks, solved.
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