Binomial theorem induction proof

[Syrus]

Homework Statement

Will someone be kind enough to check my proof (attached) of the following (also attached) theorem?

Homework Equations

The Attempt at a Solution

Oh, and as you might notice, I was beginning to run out of paper, but the binomial coefficients in the bracketed terms obviously simplify to ones in terms of r+1, as the problem statement clearly indicates.

 

[Dick]

Homework Statement

Will someone be kind enough to check my proof (attached) of the following (also attached) theorem?

Homework Equations

The Attempt at a Solution

Oh, and as you might notice, I was beginning to run out of paper, but the binomial coefficients in the bracketed terms obviously simplify to ones in terms of r+1, as the problem statement clearly indicates.

Look pretty ok to me. And sure, pointing out how the other terms are the r+1 coefficients would help.