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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 137

A geometric sequence has first term 1 and common ratio 13\frac{1}{3}31​.

ai.

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

[2]
aii.

Hence, or otherwise, evaluate

∑n=1∞(tan⁡30∘)n \sum_{n=1}^{\infty} (\tan 30^{\circ})^n n=1∑∞​(tan30∘)n
[2]
b.

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

∑n=0∞(sin⁡θ)n=22−3 \sum_{n=0}^{\infty} (\sin \theta)^n = \frac{2}{2 - \sqrt{3}} n=0∑∞​(sinθ)n=2−3​2​
[4]
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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