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Math Help - Calculus 2 Problem

  1. #1
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    Lightbulb Calculus 2 Problem

    At t = 0, there is no road obviously. After the stretch, it starts at 1000.
    At t = 1, there is 1m of road before him, 999 in front of him and after stretch 2 before him and 1998 in front of him.
    At t = 3, 3m before him, 1997 in front, after stretch 4.5 before 2995.5 in front.
    t = 4 5.5 before, 2994.5 in front; after stretch, 22/3 behind, 3992 and 2/3 in front...
    ETC. Each time I am multiplying the ratio by 2/1 and then 3/2 and then 4/3 .... etc. The denominator and numerator increased by 1 each time.
    Now obviously I need to try make a series out of this and determine if it converges of diverges to see if he will ever catch him. And then I need to come up with a general way formula for the questions for: "Can I save him sometimes,
    but not others? If and when I can save him, how long will it take in each case?" Etc.

    Now if you let d(1) [note (n) in front of d is just a subscript)] = x
    d(2) = (x+1)((n+1)/n)
    d(3) = ((x+1)((n+1))/n)+1)((n+1)/(n))
    d(4) = .......(same thing with + 1 and then multiplying by ((n+1)/(n)).

    A series is starting to develop. I'm a little stuck trying to create a geometric or harmonic series from this. Any thoughts?
    Last edited by AfterShock; October 15th 2006 at 10:51 AM.
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  2. #2
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    I just wasted 40 minutes for nothing Can you tell (without any stories) exactly the problem you are trying to solve. For example, prove convergence of this sequence -something like that.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker
    I just wasted 40 minutes for nothing Can you tell (without any stories) exactly the problem you are trying to solve. For example, prove convergence of this sequence -something like that.

    Man, I've never laughed this much in a long while!
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  4. #4
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    Quote Originally Posted by ticbol

    Man, I've never laughed this much in a long while!
    Glad to finally make you laugh. I was not trying to be funny.
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  5. #5
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    Quote Originally Posted by ThePerfectHacker
    Glad to finally make you laugh. I was not trying to be funny.
    I started reading the problem. Then I raced to its end. Then I saw your first reply. Your "I just wasted 40 minutes for nothing" walloped me.

    I could have said it myself.

    Very funny!

    -------------
    I love solving word problems. If I am not only busy somewhere everyday, I'd waste 80 minutes on that short problem. Then I'd sue AfterShock in court.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by AfterShock


    Okay- if you have made it this far, I can discuss some of my thoughts.

    At t = 0, there is no road obviously. After the stretch, it starts at 1000.

    Contradicted by:

    Iím standing at the end of a road that I somehow know is exactly 1 kilometer long.
    RonL
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  7. #7
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    Dear Inigo Montoya,

    I know this is already late, but next time that recurring nightmare bothers you again, I can suggest another way for you to avenge again your father.

    Forget about Calculus. Buy yourself a powerful riple. And silver bullets.

    Yours,
    ticbol
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