Quick questions on Sequences and series: arithmetic and geometric series and the general binomial expansion - CCEA A-Level Mathematics

4short 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 the general binomial expansion?

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Unlike the AS expansion for a positive integer power, which terminates after

n + 1

terms, the expansion for a fractional or negative power is an infinite series that only approximates the function, and only within a restricted range. Exam questions typically ask for the first three or four terms and the values of

x

for which the expansion is valid.

What is q1?

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An arithmetic sequence has

a = 5

and

d = 3

. Find the 10th term. [2 marks]

What is q2?

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A geometric series has

a = 4

and

r = \tfrac{1}{2}

. Find the sum to infinity. [2 marks]

What is q3?

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State the range of validity for the expansion of

(1 + x)^{-2}

. [1 mark]

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