Which of the following is NOT a valid application of the Binomial Theorem?
Practice Questions
1 question
Q1
Which of the following is NOT a valid application of the Binomial Theorem?
Finding the expansion of (x + y)^n.
Calculating the sum of a geometric series.
Determining coefficients in polynomial expansions.
Solving combinatorial problems.
The Binomial Theorem is specifically for polynomial expansions and does not apply to geometric series.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following is NOT a valid application of the Binomial Theorem?
Solution: The Binomial Theorem is specifically for polynomial expansions and does not apply to geometric series.
Steps: 5
Step 1: Understand what the Binomial Theorem is. It is a formula used to expand expressions that are raised to a power, like (a + b)^n.
Step 2: Identify valid applications of the Binomial Theorem. It is used for polynomial expansions, such as (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3.
Step 3: Consider what a geometric series is. A geometric series is a sum of terms where each term is a constant multiplied by the previous term, like 1 + r + r^2 + r^3 + ...
Step 4: Compare the Binomial Theorem with the geometric series. The Binomial Theorem does not apply to geometric series because it is not about expanding polynomials.
Step 5: Conclude that the Binomial Theorem is NOT valid for geometric series.
