Pascal's Triangle and Binomial Theorem

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.

Front

What are the coefficients of the 5th row in Pascal's Triangle?

Back

1, 5, 10, 10, 5, 1

Front

What is the formula for the Binomial Theorem?

Back

The Binomial Theorem states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Front

What is the 7th row of Pascal's Triangle?

Back

1, 7, 21, 35, 35, 21, 7, 1

Front

Back

Front

Back

Front

What is the relationship between the rows of Pascal's Triangle and binomial coefficients?

Back

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

Front

How do you find the nth row of Pascal's Triangle?

Back

The nth row can be found using the formula: (n choose k) = n! / (k!(n-k)!) for k = 0 to n.

Front

What is the significance of the number 1 in Pascal's Triangle?

Back

The number 1 appears at the beginning and end of each row, representing the coefficients of a^n and b^n in the binomial expansion.

Front

What is the pattern in the sums of the rows of Pascal's Triangle?

Back

The sum of the numbers in the nth row of Pascal's Triangle is equal to 2^n.