Question

If (n+1)!=90×(n-1)!,find n.​

Answer 1

 

$\displaystyle\bf\\(n+1)!=90\times (n-1)!\\\\(n-1)!\times n\times(n+1)=90\times (n-1)!~~~\Big|~:(n-1)!\\\\n(n+1)=90\\\\n(n+1)=9\times10\\\\n(n+1)=9(9+1)\\\\\implies~~\boxed{\bf n=9}$