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3.4 Sequences and Series (A-level only)

3.4 Sequences and Series (A-level only)

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Question 83

A geometric sequence has first term 1 and common ratio 0.75.

a.

(i) Find the sum to infinity, S∞S_{\infty}S∞​, of the sequence.

(ii) Hence, or otherwise, evaluate

∑n=1∞(cos⁡30∘)2n \sum_{n=1}^{\infty} (\cos 30^{\circ})^{2n} n=1∑∞​(cos30∘)2n
[3]
b.

Find the smallest positive exact value of θ\thetaθ, in radians, which satisfies the equation

∑n=0∞(2cos⁡θ)n=22−2 \sum_{n=0}^{\infty} (\sqrt{2}\cos \theta)^n = \frac{2}{2 - \sqrt{2}} n=0∑∞​(2​cosθ)n=2−2​2​
[3]
Markscheme

3.4 Sequences and Series (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.4 Sequences and Series (A-level only)

231 exam-style questions on WJEC A Level Maths 3.4 Sequences and Series (A-level only), covering 3.4.1 Sequences and Series (A-level only), 3.4.2 Sequences and Series (A-level only), 3.4.3 Sequences and Series (A-level only), 3.4.4 Sequences and Series (A-level only), 3.4.5 Sequences and Series (A-level only), 3.4.6 Sequences and Series (A-level only), and 3.4.7 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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