Question

verificati daca 6 |(1+2+3+4+.............+24)
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Answer 1

 

$\displaystyle\bf\\Exprimarea:6~\Big|~(1+2+3+4+...+24)~~~~~ (6~divide~parantza)\\\\este~echivalenta~cu:\\\\(1+2+3+4+...+24)~\vdots~6~~~~~(paranteza~este~divizibila~cu~6)\\\\Rezolvare:\\\\Calculam~suma~din~paranteza~Gauss.\\\\1+2+3+4+...+24=\frac{24(24+1)}{2}=\\\\=\frac{24\times25}{2} =12\times25=(6\times2\times25)~\vdots~6~~deoarece~un~factor~=6$