Binomial Theorem and Pascal's Triangle

Front

What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for the expansion of powers of binomials. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n.

Front

What is Pascal's Triangle?

Back

Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it, and it is used to find coefficients in binomial expansions.

Front

What is the formula for finding the coefficients in the Binomial expansion?

Back

The coefficients in the Binomial expansion can be found using the binomial coefficient, denoted as (n choose k) = n! / (k!(n-k)!), where n is the power and k is the term number.

Front

What is row 0 of Pascal's Triangle?

Back

Row 0 of Pascal's Triangle is 1.

Front

What is row 1 of Pascal's Triangle?

Back

Row 1 of Pascal's Triangle is 1, 1.

Front

What is row 2 of Pascal's Triangle?

Back

Row 2 of Pascal's Triangle is 1, 2, 1.

Front

What is row 3 of Pascal's Triangle?

Back

Row 3 of Pascal's Triangle is 1, 3, 3, 1.

Front

What is row 4 of Pascal's Triangle?

Back

Row 4 of Pascal's Triangle is 1, 4, 6, 4, 1.

Front

What is row 5 of Pascal's Triangle?

Back

Row 5 of Pascal's Triangle is 1, 5, 10, 10, 5, 1.

Front

What is the Binomial expansion of (x + 1)^2?

Back

The Binomial expansion of (x + 1)^2 is x^2 + 2x + 1.