Question

Use the defining formula for binomial coefficients to verify, for all integers 1 ≤ k ≤ n, that (n, k−1) + (n, k) = (n+1, k).

Answer 1

\[n!/(k-1)!(n-(k-1))! + n!/k!(n-k)!\]

Answer 2

then, I multiplied to get common denominators:

Answer 3

no idea what the defining formula is, but keep going, i might know this.

Answer 4

\[n!*k!(n-k)!+n!(k-1)!(n-(k-1)!/(k-1)!(n-(k-1)!k!(n-k)!\]

Answer 5

That's how far I am

Answer 6

let me upload an image

Answer 7

ok