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Math Help - analysis

  1. #1
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    analysis

    { For \  n \in N  \ let  \ \ x_n = \frac {1}{1+n} + \frac {1}{2+n} +...+\frac {1}{2n} : }
    a- \ show \  \ that   \ \ x_n  \ \ is \  \ increasing .
    b- \ prove \ \  that \  \ x_n < 1 , \  \forall n \in N .
    c- \ conclude  \ \  that \   \ x_n  \  \ is  \  \ convergent
    Last edited by flower3; September 24th 2009 at 01:31 PM.
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  2. #2
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  3. #3
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    Quote Originally Posted by flower3 View Post
    huh? what's this? are you implying we should do your homework?

    show some progress then, but, for a start, put a_n=\sum_{j=1}^n\frac1{n+j} and for 1\le j\le n we have \frac1{2n}\le\frac1{n+j}\le\frac1{n+1}.
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