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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

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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

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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:

∣x∣<32|x| < \frac{3}{2}

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