Let n and k be positive integers. After calculating several examples, guess a closed formula for: (n \ 0) + (n + 1 \ 1) + ... + (n + k \ k) If it helps, this is the formula for the sum of the nth row of the pascal triangle: (n \ 0) + (n \ 1) + .... (n \ k) = 2^n (n \ 0) means n choose 0. I couldn't write that in the forum so I had to improvise. Hopefully you know what it means. The "n" is on top and 0 is on the bottom.