Something I can't seem to prove

[Skynt]

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

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

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]

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

 

[Skynt]

obviously *bangs head* thanks!

 

[HallsofIvy]

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