Photo AI
State the values of \(|x|\) for which the binomial expansion of \((3 + 2x)^{n}\) is valid - AQA - A-Level Maths: Pure - Question 1 - 2017 - Paper 2
Question 1
State the values of \(|x|\) for which the binomial expansion of \((3 + 2x)^{n}\) is valid. Circle your answer.
Worked Solution & Example Answer:State the values of \(|x|\) for which the binomial expansion of \((3 + 2x)^{n}\) is valid - AQA - A-Level Maths: Pure - Question 1 - 2017 - Paper 2
Step 1
|x| < 3/2
Answer
The binomial expansion of ((3 + 2x)^{n}) is valid when the absolute value of (x) is less than (\frac{3}{2}). Specifically, we derive this from the requirement that the term involving (x) does not cause divergence in the binomial series.
Thus, the correct answer is given by: