1. For what values of n and r does Pascal's formula say that the number 10 in the triangle is the sum of the numbers 4 and 6?
2. Derive Pascal's formula from the fact that

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:

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