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Math Help - bounding proof question..

  1. #1
    MHF Contributor
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    bounding proof question..

    how to prove that:
    every sequence which convergences has to be bounded
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by transgalactic View Post
    how to prove that:
    every sequence which convergences has to be bounded
    A sequence \{s_n\} converges means that there exists an N and an s such that for all n>N

    |s_n-s|<1.

    Hence for all n>N:

     <br />
|s_n|-|s|\le |s_n-s| < 1<br />

    so |s_n|<1+|s|

    Therefore

    |s_n|\le \max \left[\left(\max_{0<k<N-1}|s_k|\right),1+|s|\right]

    CB
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  3. #3
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    thanks
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