Pascal’s triangle, shown next, is a triangular array of numbers in which each entry othe...

Pascal’s triangle, shown next, is a triangular array of numbers in which each entry other than a 1 is obtained by adding the two entries in the row immediately above it. For example, the first 3 in row 4 of the triangle is found by adding 1 + 2 = 3.

Find the sums of the numbers on the diagonals in Pascal’s triangle as shown next. Do you see a pattern? Explain.