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Math Help - How many terms in a geometric series

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    How many terms in a geometric series

    How many terms of the geometric sequence 1.6, -.8, .4, -.2.... must be added together starting with the first term and adding in order, so that the sum is within .001 of 16/15. So the Sum must be larger than 16/15 - .001 but smaller than 16/15 + .001. Use Algebra
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  2. #2
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    Quote Originally Posted by stones44 View Post
    How many terms of the geometric sequence 1.6, -.8, .4, -.2.... must be added together starting with the first term and adding in order, so that the sum is within .001 of 16/15. So the Sum must be larger than 16/15 - .001 but smaller than 16/15 + .001. Use Algebra
    The error in an alternating geometric series is less than the last term added

    so we need \frac{1.6}{2^n}=.001


    Solving for n gives n \approx 10.64

    so we will need to add at least 11 terms.
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    i dont see how you got that equation

    im just generally confused on what you are saying
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    Quote Originally Posted by stones44 View Post
    i dont see how you got that equation

    im just generally confused on what you are saying

    Your geometric series is this

    \sum_{n=0}^{\infty}\underbrace{1.6\left( \frac{-1}{2}\right)^n}_{a_n}=1.6-0.8+0.4-0.2+...

    Setting a_n=\mbox{error} and solve for n as above
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  5. #5
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    ok i dont get how you can set asubn = error? but

    if i did 1.6/ .5^x (instead of -.5) = .001 i solve and get -10.64
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