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idk

a guest Jan 16th, 2019 72 Never
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  1. \documentclass{article}
  2. \usepackage[utf8]{inputenc}
  3. \usepackage[T1]{fontenc}
  4. \usepackage[polish]{babel}
  5. \usepackage{amssymb}
  6.  
  7. \begin{document}
  8. \begin{itemize}
  9.  
  10.  \item
  11.  dla każdego n $\in N_+$ \[\sum_{i=1}^{n} \frac{1}{i(i+1)} = \frac{n}{n+1}\]
  12.  \item KB: dla n=1\\
  13.  L: $\frac{1}{i(i+1)} = \frac{1}{i(1+1)} = \frac{1}{2}$\\
  14.  P: $\frac{n}{n+1} = \frac{1}{1+1}$
  15.  \item Ki: Jeśli
  16.  $\frac{1}{1+...+i(i+1)} = \frac{n}{n+1}$ to $\frac{n}{n+1} + \frac{1}{(n+1)(n+2)} = \frac{n+1}{n+2}$\\
  17.  1+...+$\frac{1}{n(n+1)}=\frac{n}{n+1}$\\
  18.  P: $\frac{n+1}{n+2}$\\
  19.  L: $\frac{n}{n+1}+\frac{1}{(n+1)(n+2)}=\frac{n(n+2)+1}{(n+1)(n+2)} = \frac{n^2+2n+1}{(n+1)(n+2)} = \frac{n+1}{n+2}$\\
  20.  L = P $\square$
  21. \end{itemize}
  22.  
  23.  
  24. \end{document}
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