Sa se arate ca:
![\[\left( {1 + \frac{1}{2}} \right)\left( {1 + \frac{1}{{2^2 }}} \right) \cdot ... \cdot \left( {1 + \frac{1}{{2^n }}} \right) \le \frac{5}{2}\left( {1 - \frac{1}{{2^n }}} \right)\quad ,\forall n \in N,n \ge 2\]](https://anidescoala.ro/wp-content/ql-cache/quicklatex.com-cd7fc729cdc1bed50a707a7f17e3e228_l3.png "Rendered by QuickLaTeX.com")
M-am gandit ca trebuie demonstrat prin inductie..asa am procedat eu:
*** QuickLaTeX cannot compile formula:
\[\begin{array}{l}
.\;P(2)]
*** Error message:
\begin{array} on input line 8 ended by \end{document}.
leading text: \end{document}
Improper \prevdepth.
leading text: \end{document}
Missing $ inserted.
leading text: \end{document}
Missing } inserted.
leading text: \end{document}
Missing \cr inserted.
leading text: \end{document}
Missing $ inserted.
leading text: \end{document}
You can't use `\end' in internal vertical mode.
leading text: \end{document}
\begin{array} on input line 8 ended by \end{document}.
leading text: \end{document}
Missing } inserted.
leading text: \end{document}
Emergency stop.
Este bine?
am modificat:)..thanks