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Math Help - induction question..

  1. #1
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    induction question..

    i cant understand this step in this induction

    http://img383.imageshack.us/img383/5677/99884212ia5.gif
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  2. #2
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    It would have been clearer if you had posted the whole argument. This is part of a proof by induction of what? Actually, it looks like the result of induction.

    You know that for every n, a_n- L- \epsilon< a_{n+1}< an+ L+ \epsilon so a_n- k(L+ \epsilon)< a_{n+k}< a_n+ k(L+ \epsilon) is certainly true for k= 1. Now suppose a_n- k(L+ \epsilon)< a_n< a_{n+1}+ k(L+ \epsilon) is true for some specific k and all n. Then a_n- (k+1)(L+ \epsilon)= [a_n- (L+ \epsilon)]- k(L+\epsilon)< a_{n+1}-k(L+\epsilon)[/tex] and now use [tex]a_n- k(L+ \epsilon)< a_{n+1}[/itex] with n+1 nstead of n- which you can do because it is true for all n.
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  3. #3
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    this is a start of induction
    why they make this "k" multiplication step

    usually its just replacing K by n
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  4. #4
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    Last edited by transgalactic; January 6th 2009 at 04:37 AM.
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  5. #5
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    in the total case of K
    we are given some expression
    and we presume that its true
    so to prove the K+1 case

    from where did they use the left side development
    it seems that the are using the given expression itself to proove it
    ?
    http://img149.imageshack.us/img149/6359/10189365rk3.gif
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  6. #6
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