Pascal Triangle

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 is the first row of Pascal's Triangle?

Back

The first row is 1.

Front

How do you calculate the elements of Pascal's Triangle?

Back

Each element is calculated as the sum of the two elements directly above it.

Front

What is the Binomial Theorem?

Back

The Binomial Theorem describes the algebraic expansion of powers of a binomial. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k.

Front

What does 'n choose k' mean in the context of Pascal's Triangle?

Back

'n choose k' (denoted as C(n, k)) represents the number of ways to choose k elements from a set of n elements.

Front

What is the value of 'n choose 0'?

Back

'n choose 0' is always 1, as there is one way to choose nothing from a set.

Front

What is the value of 'n choose n'?

Back

'n choose n' is also always 1, as there is one way to choose all elements from a set.

Front

What is the sum of the elements in the nth row of Pascal's Triangle?

Back

The sum of the elements in the nth row is 2^n.

Front

What is the relationship between Pascal's Triangle and binomial expansions?

Back

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

Front

How many elements are in the nth row of Pascal's Triangle?

Back

The nth row contains n + 1 elements.