Question

determinati cel mai mare numar natural n ,astfel incat (1*2*3*4...*100) (aici vin 3 puncte) cu 3^n

Answer 1

$\displaystyle\\ (1\times2\times3\times4\times ... \times 100)~\vdots~ 3^n\\\\ \text{Exercitiul cere sa aflam de cate ori se inmulteste 3 in produsul dat.}\\\\ \text{Rezolvare:}\\\\ n=\left[\frac{100}{3}\right]+\left[\frac{100}{3^2}\right]+\left[\frac{100}{3^3}\right]+\left[\frac{100}{3^4}\right]=33+11+3+1=48\\\\ \boxed{\bf n=48}\\\\ \it \Longrightarrow ~~(1\times2\times3\times4\times ... \times 100)~\vdots~ 3^{48}\\\\ \text{Parantezele [ si ] inseamna "partea intreaga". }$