How to Prove This Combinatorial Identity Involving Binomial Coefficients?

[Four80EastFan]

Homework Statement

For positive integers n, r show that C(n+r+1, r) = C(n+r, r) + C(n+r-1, r-1) + ... + C(n+2, 2) + C(n+1, 1) + C(n, 0) = C(n+r, n) + C(n+r-1, n) + ... + C(n+2, n) + C(n+1, n) + C(n, n)

Homework Equations

The Attempt at a Solution

 

[cristo]

You need to show some work before we can help with your homework. As a start, you could try stating the definitions of e.g. C(n+r+1, r).

 

[Four80EastFan]

Sorry. I know the definition of C(n, r) = n!/[r!(n-r)!] but I still can't figure out the pattern. Are things supposed to cancel out?...other identities that I'm forgetting and could help in this question?