(n-4)! /(n-2)! >= 1/20

Question

(n-4)! /(n-2)! >= 1/20

Answer 1

(n-4)!/[(n-4)!(n-3)(n-2)]-1/20≥0
1/(n-3)(n-2)-1/20≥0
(20-n²+5n-6)/[20(n-3)(n-2)]≥0
(n²-5n-14)/[20(n-3)(n-2)]≤0
n²-5n-14=0
n1+n2=5 U n1*n2=-14⇒n1=-2 U n2=7
n-3=0⇒n=3
n-2=0⇒n=2
               +                  _                +              _                +
-----------------[-2]-------------(2)-------------(3)----------[7]----------------
-2≤n<2 U (3;7] U n∈Z<br>n∈(3;7] U {1}