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1.4 Sequences and Series

1.4 Sequences and Series

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Question 10

The function f f\,f is given by

f(x)=1+axf(x) = \sqrt{1 + ax}f(x)=1+ax​

where a a\,a is a non-zero constant.

In the binomial expansion of f(x)f(x)f(x), the coefficients of x x\,x and x2 x^2\,x2 are equal.

a.

Find the value of aaa.

[3]
b(i).

Using this value of aaa, state, using set notation, the values of x x\,x for which the binomial expansion is valid.

[1]
b(ii).

Using this value of aaa, write down the quadratic function that approximates f(x)f(x)f(x) when x x\,x is small.

[1]
Markscheme

1.4 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.4 Sequences and Series

308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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