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Math Help - limit > M, then An> M?

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    limit > M, then An> M?

    Prove:

    lim a_{n} > M --> a_{n} > M for n>>1 (large n).
    Last edited by cgiulz; September 17th 2009 at 05:57 PM.
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    Quote Originally Posted by cgiulz View Post
    Prove:

    lim a_{n} > M => a_{n} > M for n>>1.
    Does n>>1 ,mean very large n ,or n equal or greater than 1??
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    for large n.
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    Then we have:

    Since \lim_{n\rightarrow\infty} a_{n} =l>M THAT implies that for all ε>0 and hence for ε= l-M>0 ,there exists an N such that :

    for all n , n\geq N then |a_{n}-l|< l-M

    or  M-l< a_{n}-l< l-M.

    Thus  a_{n}> M for large n biger or equal to N
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