Question 1045421
To prove: {{{(matrix(2,1,n,r))+2*(matrix(2,1,n,r-1)) + (matrix(2,1,n,r-2)) = (matrix(2,1,n+2,r))}}}.


We make use of the Pascal's Triangle:  {{{(matrix(2,1,n,r)) + (matrix(2,1,n,r-1)) = (matrix(2,1,n+1,r))}}}.

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