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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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