Assume that the property shown in Figs. 1 and 2 continues to hold for subsequent rows of Pascal's triangle. Use this result to explain why the number of odd numbers in each row of Pascal's triangle is a power of 2.

In the following triangular table, known as Pascal's triangle, the entries in the nth row are the binomial coefficients

Observe that each number (other than the ones) is the sum of the two numbers directly above it. For example, in the 5th row, the number 5 is the sum of the numbers 1 and 4 from the 4th row, and the number 10 is the sum of the numbers 4 and 6 from the 4th row. This fact is known as Pascal's formula. Namely, the formula says that

Transcribed Image Text:

(c) (a) (b) (d) (b)