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Math Help - geometric series

  1. #1
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    geometric series

    hi

    I know the answer to this question is 9 but I am not sure how to get there.

    I know that there is probably a really simple method but at the moment I am making a mistake somewhere,

    2+4+8+...+512

    find the number of terms in the geometric series?


    thanks
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  2. #2
    Moo
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    Hello,

    I don't really understand. If it was a geometric series, it would have been 1/2 + 1/4 + 1/8 + ... + 1/512

    If so, you can say that 512 is 2^9
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  3. #3
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    geometric series re

    those are the number that it shows in the book, could be wrong though.

    I know that 2^9 is 512 but how do I find the number of terms in the series- is there a really simple step that I am missing?

    thanks
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    the nth term of a geometric series is ar^(n-1). since the last term is 512 and we know that a=2 and r=2

    substituting values

    2(2)^(n-1) = 512
    2^(n-1) = 256
    2^(n-1) = 2^8

    compare both sides

    n-1 = 8
    n= 9

    hence the last term is the 9th term
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  5. #5
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    Quote Originally Posted by soso View Post
    those are the number that it shows in the book, could be wrong though.

    I know that 2^9 is 512 but how do I find the number of terms in the series- is there a really simple step that I am missing?

    thanks
    Well,

    You have :

    2^1, 2^2, 2^3, ..., 2^9

    This makes 9 termes
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    \sum\limits_{k = 1}^N {a^k }  = \frac{{a - a^{N + 1} }}{{1 - a}},\quad N = 9\,\& \,a = 2<br />
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  7. #7
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    thanks

    thanks for the help
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