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Thread: Divergent and Convergent

  1. #1
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    Divergent and Convergent

    Can someone please help me with the following question:

    Divergent and Convergent-122333333.jpg


    Thanks


    Nerdo
    Last edited by nerdo; Oct 25th 2009 at 08:15 AM.
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  2. #2
    Junior Member utopiaNow's Avatar
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    a) Proof: Given arbitrary $\displaystyle \epsilon > 0$, choose $\displaystyle N$ such that both these inequalities hold: $\displaystyle N > 100$ and $\displaystyle N > \frac{1}{\epsilon}$. Then we know $\displaystyle \forall n \geq N$, $\displaystyle x_n = 1/n < \epsilon$. Hence $\displaystyle x_n \rightarrow 0$.

    b) Follows pretty easily from a. you should be able to handle it.
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  3. #3
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    Quote Originally Posted by utopiaNow View Post
    a) Proof: Given arbitrary $\displaystyle \epsilon > 0$, choose $\displaystyle N$ such that both these inequalities hold: $\displaystyle N > 100$ and $\displaystyle N > \frac{1}{\epsilon}$. Then we know $\displaystyle \forall n \geq N$, $\displaystyle x_n = 1/n < \epsilon$. Hence $\displaystyle x_n \rightarrow 0$.

    b) Follows pretty easily from a. you should be able to handle it.

    Thanks for the help
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