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1.4 Sequences and Series

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Question 32

Let Q(n)=∑k=0nk4−∑k=0n−1k4Q(n) = \sum_{k=0}^{n} k^4 - \sum_{k=0}^{n-1} k^4Q(n)=∑k=0n​k4−∑k=0n−1​k4 where nnn is a positive integer.

a.

Find Q(2)Q(2)Q(2) and Q(5)Q(5)Q(5).

[3]
b.

Solve the equation Q(n)=2.56×1010Q(n) = 2.56 \times 10^{10}Q(n)=2.56×1010.

[3]
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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