Algrebra 2 help

Question

Show that the sum of the 34th and 35th numbers in the 117th row of the pascal's triangle is equal to the 85th number in the 118th row of the triangle

Answer 1

I am not sure how you are counting the rows and columns in Pascal's triangle,but I think the identity you are looking for is this:

_nC_{r-1 + n}C_{r = n+1}C_r which is easy to prove by writing out the definitions of each term and then doing some algebra. For your particular problem remember that _nC_r = _nC_n-r.

Oh, _nC_r is n!/[r!(n-r)!], the binomial coefficient of n and r which are the numbers is Pascal's triangle.