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Thread: demonst.

  1. #1
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    demonst.

    Demonstrate that:
    $\displaystyle \
    \ln n < \sum\limits_{k = 1}^n {\frac{1}{k}} < \ln (n + 1)
    \
    $
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  2. #2
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    Quote Originally Posted by Ortega View Post
    Demonstrate that:
    $\displaystyle \
    \ln n < \sum\limits_{k = 1}^n {\frac{1}{k}} < \ln (n + 1)
    \
    $
    Consider the function $\displaystyle f(x) = \frac{1}{x}$ and find the area from $\displaystyle [1,n]$ by integral and now find the area by approximated rectangles of width $\displaystyle 1$. Now compare results.
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