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Sequences and Series

Quick questions on Binomial expansion for rational index explained: H2 Mathematics Sequences and Series

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is not factoring out the constant?
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(4+x)1/2(4 + x)^{1/2} must become 2(1+x4)1/22(1 + \frac{x}{4})^{1/2} before expanding; expanding (4+x)(4 + x) directly is wrong.
What are sign errors with negative indices?
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The coefficients n(n−1)⋯n(n-1)\cdots alternate in sign for negative nn; compute them carefully term by term.
What is q1?
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Expand (1−x)1/2(1 - x)^{1/2} up to the term in x2x^2. [3 marks]
What is q2?
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State the range of validity of the expansion of (1+4x)−1(1 + 4x)^{-1}. [1 mark]
What is q3?
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Write (9+x)1/2(9 + x)^{1/2} in a form ready for the binomial expansion. [2 marks]

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