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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 165

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∞(sin⁡60∘)2n \sum_{n=1}^{\infty} (\sin 60^{\circ})^{2n} n=1∑∞​(sin60∘)2n
[5]
b.

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

∑n=0∞(tan⁡θ)n=33−3 \sum_{n=0}^{\infty} (\tan \theta)^n = \frac{3}{3 - \sqrt{3}} n=0∑∞​(tanθ)n=3−3​3​
[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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