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Questions and Answers
What does 'n choose k' represent in the binomial theorem formula?
What does 'n choose k' represent in the binomial theorem formula?
- The exponent for the term in the binomial expansion
- The sum of the binomial coefficients for a given n
- The factorial of n divided by the factorial of k
- The number of ways to choose k elements from a set of n elements (correct)
What is the formula for the binomial theorem?
What is the formula for the binomial theorem?
- (a + b)^n = Σ(n choose k) * a^k * b^(n-k), where k ranges from 0 to n
- (a + b)^n = Σ(n choose k) * a^(n-k) * b^k, where k ranges from 0 to n (correct)
- (a - b)^n = Σ(n choose k) * a^k * (-b)^(n-k), where k ranges from 0 to n
- (a - b)^n = Σ(n choose k) * a^(n-k) * (-b)^k, where k ranges from 0 to n
What is the relationship between the binomial theorem and Pascal's triangle?
What is the relationship between the binomial theorem and Pascal's triangle?
- The terms in the binomial expansion are arranged in a pattern similar to Pascal's triangle
- Pascal's triangle provides an alternative method for expanding binomial expressions
- The coefficients in the binomial expansion can be found in Pascal's triangle (correct)
- Pascal's triangle can be used to calculate the value of 'n choose k'
