Sigma notation

Paper 2: Pure Mathematics 2 June 2024, Question 4 Paper 2: Pure Mathematics 2 · June 2024 · Question 4 5 marks

A sequence u₁, u₂, u₃,... is defined by

where k is a positive constant.

Given that u₃ = –1

(a)

show that

[2]

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(b)(i)

find the value of k,

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(b)(ii)

[3]

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Paper 2: Pure Mathematics 2 June 2022, Question 3 Paper 2: Pure Mathematics 2 · June 2022 · Question 3 4 marks

(a)(i)

Show that this sequence is periodic.

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(a)(ii)

State the order of this periodic sequence.

[2]

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(b)

Find the value of

[2]

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Paper 2: Pure Mathematics 2 October 2021, Question 9 Paper 2: Pure Mathematics 2 · October 2021 · Question 9 3 marks

Also involves Exact trigonometric values

Show that

[3]

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Paper 2: Pure Mathematics 2 June 2019, Question 8 Paper 2: Pure Mathematics 2 · June 2019 · Question 8 6 marks

Also involves Laws of logarithms

(i)

Find the value of

[3]

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(ii)

Show that

[3]

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Paper 2: Pure Mathematics 2 June 2018, Question 4 Paper 2: Pure Mathematics 2 · June 2018 · Question 4 7 marks

(i)

4.

[4]

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(ii)

A sequence u₁, u₂, u₃, … is defined by

[3]

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