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Thread: Sequences

  1. #1
    Super Member Showcase_22's Avatar
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    Sequences

    I have another post about sequences but this question seems easier (hence why I posted it here!).

    However, "easier" is used relative to the other question I am stuck on (posted in Advanced Algebra).

    The problem is:

    Think of an example to show that the statement,

    if $\displaystyle (a_n) \rightarrow 0$ then $\displaystyle \frac{1}{a_n} \rightarrow \infty$

    is false, even if $\displaystyle a_n \neq 0$ for all n
    All the equations I have tried have failed. I can't think of a method to do this question properly =(

    Any ideas would be greatly appreciated!
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  2. #2
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    $\displaystyle \left[ {\frac{{\left( { - 1} \right)^n }}
    {n}} \right] \to 0$

    But what about $\displaystyle \frac{1}
    {{\left| {a_n } \right|}}$?
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  3. #3
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    Exactly.

    Think of a non-monotonic sequence that tends to zero, ie. that approaches zero from the "-ve and the +ve side".

    (-1)^n/n is a good example.
    Last edited by nmatthies1; Oct 10th 2008 at 12:31 PM.
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  4. #4
    Super Member Showcase_22's Avatar
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    I thought of it that way but couldn't quite grasp the concept.

    I was trying sequences like $\displaystyle a_n=\frac{sin n}{n}$. Unfortunately this equals zero so it didn't work!

    thanks for the help guys!
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  5. #5
    Super Member Showcase_22's Avatar
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    lol, I didn''t see it!

    boy is my face red!

    So have you done the section about $\displaystyle \pi$ yet? It's really confusing!

    (check my other thread in the advanced algebra section).
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  6. #6
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    Not worry it happens to all of us.
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