Question

Rezolvati inecuatiile:
b) (x+1)!-x!<=100

Answer 1

Răspuns:

x ∈ {0, 1, 2, 3, 4}

Explicație pas cu pas:

x ∈ N

$(x + 1)! -x! \leqslant 100 \\ x!(x + 1) - x! \leqslant 100 \\ x!(x + 1 - 1) \leqslant 100 \\ x!x \leqslant 100$

$\implies x \in \Big\{ 0; 1; 2; 3; 4 \Big\}$