Pascals Triangle

Front

What is Pascal's Triangle?

Back

A triangular array of the binomial coefficients, where each number is the sum of the two directly above it.

Front

What is the formula for finding the nth row of Pascal's Triangle?

Back

The nth row corresponds to the coefficients of the expansion of (a + b)^n.

Front

What are binomial coefficients?

Back

The coefficients in the expansion of a binomial expression, represented as C(n, k) or n choose k.

Front

How do you calculate a binomial coefficient C(n, k)?

Back

C(n, k) = n! / (k!(n-k)!) where n! is the factorial of n.

Front

What is the value of C(5, 2)?

Back

C(5, 2) = 5! / (2!(5-2)!) = 10.

Front

What is the relationship between the rows of Pascal's Triangle and powers of binomials?

Back

The nth row of Pascal's Triangle gives the coefficients for the expansion of (a + b)^n.

Front

What is the first row of Pascal's Triangle?

Back

The first row is 1.

Front

What is the second row of Pascal's Triangle?

Back

The second row is 1, 1.

Front

What is the third row of Pascal's Triangle?

Back

The third row is 1, 2, 1.

Front

What is the fourth row of Pascal's Triangle?

Back

The fourth row is 1, 3, 3, 1.