Add each of the first five rows of Pascal's triangle, as indicated. Do you see a pattern? 1+1=2, 1+2+1=4, 1+3+3+1=8, 1+4+6+4+1=16, 1+5+10+10+5+1=32. On the basis of the pattern you have found, find the sum of the nth row: [n; 0] + [n; 1] + [n; 2] + … + [n; n]. Prove your result by expanding (1+1)^n using the Binomial Theorem.