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Math Help - Mathematical Induction

  1. #1
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    Mathematical Induction

    Hi, i have been reading a mathematical indcution book and i start answering the exercises but i think i have a problem with this one, I'll be grateful if you help

    # Problem
    Determine Un if we know that U1=1 and Uk=Uk-1 + 3. for K>1.
    suggestion: U1=3*1 - 2, U2=3*2 - 2
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  2. #2
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    Re: Mathematical Induction

    Quote Originally Posted by mcolula View Post
    Hi, i have been reading a mathematical indcution book and i start answering the exercises but i think i have a problem with this one, I'll be grateful if you help

    # Problem
    Determine Un if we know that U1=1 and Uk=Uk-1 + 3. for K>1.
    suggestion: U1=3*1 - 2, U2=3*2 - 2
    In other words, they "suggest" that the general formula is Un= 3n- 2[/sub].
    All you need to do is show that this does, in fact, satisfy the recursion.
    If Un= 3n- 2, then Uk-1= 3(k- 1)- 2= 3k- 5, Uk= 3k- 2 and it is certainly true that Uk= 3k- 2= 3k- 5+ 3= U[sub]k-1]+ 3
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  3. #3
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    Re: Mathematical Induction

    Mathematical Induction-30-may-13.png
    Thanks from mcolula
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  4. #4
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    Re: Mathematical Induction

    I found the solution to this problem on my book, i just need one more thing, the solution on the book is:

    1 - the hypothesis is valid for N=1
    2 - with Uk = 3k-2

    then

    Uk+1 = Uk + 3 = 3k - 2 + 3 = 3(k+1) - 2 //This is the solution

    I just want someone explain me why Uk+1 is equal to Uk + 3 especially why that three.


    thanks for your help.
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  5. #5
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    Re: Mathematical Induction

    It is what you have been given in the question.
    Determine Un if we know that U1=1 and Uk=Uk-1 + 3. for K>1.
    just replace k by k+1
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