Something I can't seem to prove...

**Skynt** · Jun29-09, 10:33 PM

It should be really simple, but I think the algebra is bogging me down:

$LaTeX Code: \\frac{n!}{(n-i)! i!} + \\frac{n!}{[n-(i+1)]! (i+1)!} = \\frac{(n+1)!}{(n-i)! (i+1)!}$

Can anyone show me the process of proving this? I don't see how the two expressions are equal...

essentially I can't get rid of the [n - (i + 1)]! term when I try to combine the two fractions and expand things.

**CRGreathouse** · Jun30-09, 01:19 AM

Notice that [n - i] * [n - (i + 1)]! = [n - i]!.

**Skynt** · Jun30-09, 03:52 AM

obviously *bangs head* thanks!

**HallsofIvy** · Jun30-09, 06:36 AM

That is, by the way, the formula used for producing Pascal's triangle.