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1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 171

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

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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