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Math Help - Negative logarithm while finding limiting difference

  1. #1
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    Negative logarithm while finding limiting difference

    Hi Guys,

    I hit a dead end while solving this problem. I haven't done Complex numbers so far, so I am not sure how to proceed.

    By using logarithms, find approximately the difference between \dfrac{a}{1 - r} and \dfrac{a(1 - r^n)}{1 - r} where,

    a = 2, r = -0.7, n = 1001

    I used the difference formula,
    <br />
D = \dfrac{ar^n}{r - 1}<br />

    and substituting for a, r and n, I got,

    D = \dfrac{2(-0.7)^{1001}}{1.7}

    But for the -0.7 I could have used the logarithm identities to solve this. But I can't take log -0.7. The required answer is -1.032 \times 10^{-155}

    How do I proceed? Thanks again for your help!

    Edit:
    I went back and calculated S and S_{\infty} individually, They are both identical =1.176. Hence the difference would be 0. Is the textbook answer wrong?
    Last edited by mathguy80; April 13th 2011 at 07:51 AM. Reason: Fixed question
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  2. #2
    Moo
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    Hello,

    You are asked to compute D-\frac{a}{r-1}, not D alone.
    At the moment, I can't see why you're asked to use the logarithm... Anyway, (-0.7)^{1001}=-(0.7)^{1001}, if it can be of any help...
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,

    You are asked to compute D-\frac{a}{r-1}, not D alone.
    Sorry @Moo, I typed that in word form incorrectly, the question was difference of

    \dfrac{a}{1 - r} and \dfrac{a(1 - r^n)}{1 - r}

    I've edited the question, It still has the negative logarithm.
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