Question

In cate zerouri se termina numarul n=1 X 2 X 3 X 4 X......X30

Answer 1

$\displaystyle Pentru~a~calcula~in~cate~zerouri~se~termina~numarul \\ \\ 1 \cdot 2 \cdot 3 \cdot... \cdot n,~folosesti~urmatoarea~formula: \\ \\ \left[ \frac{n}{5}\right]+\left[ \frac{n}{5^2}\right]+\left[ \frac{n}{5^3}\right]+... \\ \\ In cazul~de~fata~avem: \\ \\ \left[ \frac{30}{5}\right]+\left[ \frac{30}{5^2}\right]+\left[ \frac{30}{5^3}\right]+...=6+1+0+0+0+...=7~zerouri. \\ \\ \left[ x \right]=partea~intreaga~a~numarului~real~x.$