Question

Determinati in câte zerouri se termina produsul 5!x15!x25!x35! Va rog frumos repede

Answer 1

5!×15!×25!×35! se termină în:

$\displaystyle \sum\limits_{k=1}^{\infty}\left\lfloor \dfrac{5}{5^k}\right\rfloor+\sum\limits_{k=1}^{\infty}\left\lfloor \dfrac{15}{5^k}\right\rfloor+\sum\limits_{k=1}^{\infty}\left\lfloor \dfrac{25}{5^k}\right\rfloor+\sum\limits_{k=1}^{\infty}\left\lfloor \dfrac{35}{5^k}\right\rfloor= \\ \\ = 1+3+(5+1)+(7+1) = 4+6+8 = 18\text{ zerouri}$