Property of the Pascal Triangle

Another interesting property of the Pascal Triangle.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1

Since Choose(n,k) = (k+1)/(n-k)*Choose(n,k+1) we get ( for example ) for row 7:
1/7 * 7 = 1
2/6 * 21 = 7
3/5 * 35 = 21
4/4 * 35 = 35
5/3 * 21 = 35
6/2 * 7 = 21
7/1 * 1 = 7