Question 1045420
If you are trying to prove {{{(matrix(2,1,n-1,r-1)) + (matrix(2,1,n,r-1)) = (matrix(2,1,n,r)) }}}, then forget it, it's not true.


For instance, {{{(matrix(2,1,10,3)) + (matrix(2,1,11,3)) = 285 <> 330= (matrix(2,1,11,4)) }}}.


What is true is the relation  


{{{(matrix(2,1,n-1,r-1)) + (matrix(2,1,n-1,r)) = (matrix(2,1,n,r)) }}}, 


which is the basis for Pascal's Triangle.