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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 176

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]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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