Question

Să se afle n, dacă Pn. A +3=30(n+1)

Answer 1

$\it P_n\cdot A_{n+3}^3=30(n+1)! \Rightarrow n!\cdot\dfrac{(n+3)!}{n!}=30(n+1)! \Rightarrow (n+3)!=30(n+1)! \Rightarrow \\ \\ \Rightarrow (n+1)! (n+2)(n+3)=30(n+1)! \Rightarrow (n+2)(n+3)=30=5\cdot6 \Rightarrow \\ \\ \Rightarrow n+2=5 \Rightarrow n=3$