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Thread: Analysis

  1. #1
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    Question Analysis

    Let Xn and Yn be two series of real numbers such that Xn<Yn for all n>N.

    Show that
    a)lim inf Xn<lim inf Yn
    b)lim supXn<lim sup Yn
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  2. #2
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    Quote Originally Posted by hebby View Post
    Let Xn and Yn be two series of real numbers such that Xn<Yn for all n>N.

    Show that
    a)lim inf Xn<lim inf Yn
    b)lim supXn<lim sup Yn

    Both inequalities are false: \frac{n-1}{n}<\frac{n+1}{n}\,\,\,\forall\,\,n\in\mathbb{N}, but there's equality in (a) and in (b) since the limit exists in both cases and is thus equal to the lower and upper limits.

    Tonio
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