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Math Help - Integral of geometric series

  1. #1
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    Integral of geometric series



    Hint: Cal II stuff; what is a geometric series? Try converting the integrand to something simpler.


    I don't even know where to begin with this one. The hint isn't helping me. I know what a geometric series is, but I'm not sure how to find the integral of this, or how to convert it into something that I can find the integral.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ban26ana View Post


    Hint: Cal II stuff; what is a geometric series? Try converting the integrand to something simpler.


    I don't even know where to begin with this one. The hint isn't helping me. I know what a geometric series is, but I'm not sure how to find the integral of this, or how to convert it into something that I can find the integral.
    You know what is a geometric series, so I suppose you know the formula to compute it. use that formula to convert the series into an algebraic expression which you can integrate. the series in the integral is actually equal to \frac 1{1 - x}
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  3. #3
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    Quote Originally Posted by ban26ana View Post


    Hint: Cal II stuff; what is a geometric series? Try converting the integrand to something simpler.


    I don't even know where to begin with this one. The hint isn't helping me. I know what a geometric series is, but I'm not sure how to find the integral of this, or how to convert it into something that I can find the integral.
    A geometric series \sum_{k = 0}^{\infty}ar^{k} = \frac{a}{1 - r} as long as |r| < 1.


    So in your case \sum_{k = 0}^\infty x^k = \frac{1}{1 - x}, provided |x| < 1.

    From the limits of your integral, we can see that 0 \leq x \leq \frac{1}{2}, so the condition |x| < 1 is satisfied.



    So you are really trying to evaluate

    \int_0^{\frac{1}{2}}{\frac{1}{1 - x}\,dx}
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    Thank you for showing me the obvious. For some reason I was confusing x with k, and trying to put the values 0 and 1/2 as k values...we'll just say it's almost 4 am and I may need some coffee. Thanks!
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