# demonst.

• September 24th 2008, 12:41 PM
Ortega
demonst.
Demonstrate that:
$\
\ln n < \sum\limits_{k = 1}^n {\frac{1}{k}} < \ln (n + 1)
\
$
• September 24th 2008, 12:59 PM
ThePerfectHacker
Quote:

Originally Posted by Ortega
Demonstrate that:
$\
\ln n < \sum\limits_{k = 1}^n {\frac{1}{k}} < \ln (n + 1)
\
$

Consider the function $f(x) = \frac{1}{x}$ and find the area from $[1,n]$ by integral and now find the area by approximated rectangles of width $1$. Now compare results.