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Math Help - Inductin guidance

  1. #16
    MHF Contributor Also sprach Zarathustra's Avatar
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    Good-Luck Nicolase!
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  2. #17
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    Hrm doing the same thing for an=1+(-1)^N I get
    an=1+(-1)^n
    a1=1+(-1)^1=0
    a2=1+(-1)^2=2
    a3=1+(-1)^3=0
    a4=1+(-1)^4=2

    but when I tried following what you have done I end up, again, unbalanced.
    1+(-1)^n=1+(-1)^n+1 (I assumed) Will check in the morning, brain about to explode. thanks again.
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  3. #18
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    Still have an issue with the last message posted. Am I correct in saying that the ratio is: 2?
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  4. #19
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by Nickolase View Post
    Still have an issue with the last message posted. Am I correct in saying that the ratio is: 2?

    Hmmm...

    Look at this:

    a_{n+1}+a_n=2

    seems me right...

    Prove it! You know how!
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  5. #20
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    Quote Originally Posted by Nickolase View Post
    Give a recursive definition of the sequence {an},n=1,2,3.....if an=4n-2 (The An's are sub n's, just not sure how to do that yet) all the information that is given. If necessary I can post the other similar problem with answer.
    Find that: a_1=2,~a_2=6,~a_3=10.
    So it seems that a_1=2 and if n>1 then a_n=a_{n-1}+4.
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  6. #21
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Hmmm...

    Look at this:

    a_{n+1}+a_n=2

    seems me right...


    Prove it! You know how!
    This brings up one of the questions that confuses me. Can I use induction to prove recursive? Or are the two completely unrelated? Also. it seems that while I was able to do the work, my remaining confusion seems to be the manner in which the formula is expressed when finished, which seems different than what I started with. I don't believe it matters as the other examples in the section seem to be looking for the ratio: which I believe to be correct. However, I want to know for the sake of knowing because while passing the course is the priority, full understanding is the goal. I dislike being on the outside looking in.

    Itried to use induction but it doesn't seem to add up correctly so either I can't do it, or I'm doing something wrong almost immediately.

    p(1) 1+2+3...1+(-1)^1=1
    0=1 False but true if p(0)
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  7. #22
    MHF Contributor Also sprach Zarathustra's Avatar
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    I think it's depends when or where use induction...

    Usually in this type of questions better use these steps...

    If you had some a_n=f(n) : ( a_n is not in recursive form) and you need to find a recursive formula for a_n.

    So, first of all: Try to find a pattern

    second: try to guess recursive formula!

    third: Check if your guess been successful guess by "putting" your a_n=f(n)

    ------------------------------------------------------------------------

    In your last problem:

    a_n=1+(-1)^n

    so, our sequence is: 0,2,0,2,0,...

    Finding pattern:

    We can see that:

    a_2-a_1=2
    a_4-a_3=2

    Now is the time for guessing!

    We guess that our recursive formula(s) looks like: a_{n+2}=a_n

    with a_0=2 and a_{n+3}=a_{n+1}

    with a_0=0

    To prove these formulas you need to substitute a_n=1+(-1)^n in each of them.


    I hope you understood something from all this...
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  8. #23
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    Thanks to everyone. It may not seem like I'm getting it, but I am, slowly but surely. Problem with that statement is that it is a six week course.
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