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Albastrica321
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in cate zerouri se termina numărul : 1.2.3.4........74.75 ?


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Răspuns :

Albastruverde12
[tex]\displaystyle Exista~o~formula:~Numarul~n!=1 \cdot 2 \cdot 3 \cdot ... \cdot n~se \\ \\ termina~in~ \left[ \frac{n}{5} \right]+ \left[ \frac{n}{5^2} \right]+ \left[ \frac{n}{5^3} \right]+...~zerouri. \\ \\ \left[x \right ]=partea~intreaga \\ \\ Deci~numarul~1 \cdot 2 \cdot 3 \cdot ... \cdot n~se~termina~in \\ \\ \left[ \frac{75}{5} \right]+ \left[ \frac{75}{25} \right] +\left[ \frac{75}{125} \right]+...=15+3+ \underbrace{0+...}_\mbox{doar~zerouri}}=18~zerouri.[/tex]

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