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    Gilgames's Avatar
    Gilgames Posts: 6, Reputation: 1
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    #1

    Dec 5, 2006, 05:39 AM
    Prove by induction
    I need to prove by induction that for every n => 0,
    8/1*3 + 8/5*7 +... + 8/(4n+1)*(4n+3) <= 4

    Every help is welcome!
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #2

    Dec 5, 2006, 05:45 AM
    do you know how to calculate the sum of an infinite series?

    If you can show that the sum to infinity of the progression is less than or equal to 4, then you can argue that every other sum is less than four (although this isn't induction)
    Gilgames's Avatar
    Gilgames Posts: 6, Reputation: 1
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    #3

    Dec 5, 2006, 10:17 AM
    Quote Originally Posted by Capuchin
    do you know how to calculate the sum of an infinite series?

    If you can show that the sum to infinity of the progression is less than or equal to 4, then you can argue that every other sum is less than four (although this isnt induction)
    It is okay, I've found it! Thank you for your immediate reply! You can indeed solve it by induction. For n = 0, it's true, since 8/3 < 4. Let's suppose it holds true for n=k. Then we have to show that it's true for n=k+1. I had to rewrite the whole series, adding 8/[4(k+1)+1][4(k+1)+3], and get this on the other side. Then all that remains is calculating the result, which proves what we had supposed earlier! Thx anyway!

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