Question

Care e formula la Ex: 1x2x3x...x20 ???
Cum se numeste aceasta formula???
Formula as vrea sa o aflu. Pls..
Dau 10 puncte!

Answer 1

$Nu~este~nicio~formula~pentru~calcularea~acelui~produs.~Tie~ti~se~ \\ \\ cere~cu~siguranta ~sa~afli~numarul~de~0-rouri~cu~care~se~termina. \\ \\ Iar~pentru~acest~lucru,~exista~intr-adevar~o~formula: \\ \\ "n!=1 \cdot 2 \cdot 3 \cdot ... \cdot n~se~termina~in~ \\ \\ \Big[ \frac{n}{5} \Big]+ \Big[\frac{n}{5^2} \Big]+ \Big[\frac{n}{5^3} \Big] +...~(urmeaza~o~infinitate~de~termeni,~caci~de~la~ \\ \\ un ~moment~dat~toti~vor~fi~nuli~(0+0+0+...)~.$

$Numarul~20!=1 \cdot 2 \cdot 3 \cdot ... \cdot 20~se~termina~in: \\ \\ \Big[ \frac{20}{5} \Big]+ \Big[\frac{20}{5^2} \Big] + \Big[ \frac{20}{5^3} \Big]+...=4+0+0+...=4~zerouri. \\ \\ * [x]=partea~intreaga~a~lui~x \\ \\ VARIANTA~MAI~SIMPLA \\ \\ Exponentul~lui~2~din~acest~produs~este~mai~mare~decat~exponentul~ \\ \\lui~5 \Rightarrow~numarul~de~zerouri~este~dat~de~puterea~lui~5.$

$Multiplii~de~5~din~produs~sunt:~5=5 \cdot 1,~10=5 \cdot 2,~15=5 \cdot 3~si \\ \\ 20=5 \cdot 4 \Rightarrow puterea~lui~5~este~4~ \Rightarrow 4~zerouri.$