Question

Determine o valor de n nas equações:
A)(n+2)!+(n+1)!=15n!

Answer 1

$(n+2)!+(n+1)!=15n!\\\\(n+2)(n+1)n!+(n+1)n!=15n!\\\\n!((n+2)(n+1)+(n+1))=15n!\\\\(n+2)(n+1)+(n+1)=15\\\\n^2+3n+2+n+1=15\\\\n^2+4n+3=15\\\\n^2+4n-12=0\\\\(n+6)(n-2)=0\\\\n=2\ ou\ n=-6$

Como nao existe fatorial de numeros negativos pares a resposta eh apenas n=2