simple yet clever proof with factorials

we're supposed to use the principle of mathematical induction for this.

http://dl.getdropbox.com/u/594924/fac.jpg

basically the inductive part boils down to proving algebraically that

but i'm not familiar enough with factorials to show this. i've read about factorials on wikipedia but they didn't have any good identities or anything i could use. any suggestions would be very helpful but for now i'm going to just stare at it for a few minutes and read about series with factorials.

thanks guys