Question

n!/ (n+2)!+(n+1)!=1/48

Answer 1

n!/ (n+2)! + (n+1)!=1/48

n!/ (n+2)(n+1)n! + (n+1)n!=1/48

n!/ n![(n+2)(n+1)+ (n+1) =1/48

1/(n+2)(n+1)+(n+1) =1/48

(n+2)(n+1)+(n+1) = 48

n²+3n+2 + n+1=48

n²+4n+3 -48=0

n² +4n -45=0

∆= 16 +180 = 196 => √∆=14

n = -b+√∆/2a = -4+14/2 = 10/2 = 5 ✓