In the k+1 step they all turn into (k+1)C1 which means you can split them into kC1+kC0 etc repeatedly until you’ll find you’ve got double the assumption, which is 2*2^k which is 2^(k+1)
In the k+1 step they all turn into (k+1)C1 which means you can split them into kC1+kC0 etc repeatedly until you’ll find you’ve got double the assumption, which is 2*2^k which is 2^(k+1)