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  1. #1
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    Question on induction

    I have these 2 questions from my discrete Math assignment and i can't figure out how to deal with it. Inexperienced friends of mine say that the question is wrong. Can anyone help me solve it?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by freeze_sr View Post
    I have these 2 questions from my discrete Math assignment and i can't figure out how to deal with it. Inexperienced friends of mine say that the question is wrong. Can anyone help me solve it?
    Well they both make no sense, the first one should be:

    Show that for integers n\ge 3:

    2n+1 < 2^n

    RonL
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by freeze_sr View Post
    I have these 2 questions from my discrete Math assignment and i can't figure out how to deal with it. Inexperienced friends of mine say that the question is wrong. Can anyone help me solve it?
    hehe, your questions are wrong. the first is not an inequality, it should read 2n + 1 ~{\color{red} < }~2^n for n = 3,4, \dots. the second question has no real solutions, much less integer solutions.

    for the first, here are the steps:

    Let P(n):~2n + 1 < 2^n for n = 3,4, \dots

    Verify that P(3) holds. this is your base case.

    Now assume P(n) holds, and show that P(n + 1) holds.

    that is, assume 2n + 1 < 2^n and show that it implies 2(n + 1) + 1 < 2^{n + 1}

    good luck!
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    Ok thanks.
    I'll now have to see my lecturer on these errors.
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  5. #5
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    For the second one, I think that the parentheses are meant to be "integer part" symbols:

    \left\lfloor\frac{\lambda^2}4\right\rfloor = \left\lfloor\frac{\lambda-1}2\right\rfloor\, \left\lfloor\frac{\lambda+1}2\right\rfloor

    This is true when λ is an odd integer. In fact, if λ = 2k+1 then both sides are equal to k(k+1).
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    opalg,

    Is there a solution for the second question?
    Is λ = 2k+1 the final answer?
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  7. #7
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    OK, according to my lecturer, the first question is correct.
    The question requires me to prove that it is wrong.
    The second question had a missing word and should read
    " Show that if lambda is an odd integer"
    Could you help me out?
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by freeze_sr View Post
    OK, according to my lecturer, the first question is correct.
    The question requires me to prove that it is wrong.
    The second question had a missing word and should read
    " Show that if lambda is an odd integer"
    Could you help me out?
    Please repost what you think the questions now are.

    RonL
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  9. #9
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    Resolved

    Nevermind. It's obvious that these questions have errors. I will have to come up with something.
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