BINOMIAL EXPANSION AND PASCALS TRIANGLE

Front

What is a binomial?

Back

A polynomial of the sum or difference of two terms.

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

How many terms are in the expansion of (1+b)^5?

Back

6

Front

What is the general term in the binomial expansion of (a+b)^n?

Back

The general term is given by T(k+1) = C(n,k) * a^(n-k) * b^k, where C(n,k) is the binomial coefficient.

Front

What is the binomial coefficient C(n,k)?

Back

C(n,k) = n! / (k!(n-k)!), representing the number of ways to choose k elements from a set of n elements.

Front

What is the probability of getting 4 strikes and 2 spares in 6 frames if the probability of a strike and a spare is equal?

Back

23%.

Front

What is the second term of (3x-y)^5?

Back

243x^4y.

Front

How do you find the coefficient of a specific term in a binomial expansion?

Back

Use the binomial theorem and the formula for the general term.

Front

What is the expansion of (p+q)^n?

Back

The expansion is given by the sum of C(n,k) * p^(n-k) * q^k for k=0 to n.

Front

What is the significance of the coefficients in Pascal's Triangle?

Back

They represent the coefficients in the binomial expansion of (a+b)^n.