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Proof by mathematical induction — Question 5

QCAA 2025, Paper 1 · 1 mark

Q5 · 2025 · Technology-freeSimple familiar1 mark

QUESTION 5

Within the method of proof using mathematical induction, for which sum is the initial statement true?
(A)
∑i=1ni3=n2(n+1)2\displaystyle\sum_{i=1}^{n}i^3=n^2(n+1)^2
(B)
∑i=1ni3=2n2(n+1)2\displaystyle\sum_{i=1}^{n}i^3=2n^2(n+1)^2
(C)
∑i=1ni3=n2(n+1)22\displaystyle\sum_{i=1}^{n}i^3=\frac{n^2(n+1)^2}{2}
(D)
∑i=1ni3=n2(n+1)24\displaystyle\sum_{i=1}^{n}i^3=\frac{n^2(n+1)^2}{4}
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