| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Topic | Proof by induction |
| Type | Prove summation formula |
| Difficulty | Moderate -0.3 This is a standard proof by induction of a well-known summation formula (sum of cubes). It requires routine application of the induction framework with straightforward algebra, making it slightly easier than average. The formula is given, so no discovery is needed, and the algebraic manipulation is mechanical. |
| Spec | 4.01a Mathematical induction: construct proofs |
4. Prove by induction that the sum of the first $n$ cube numbers is $\frac { 1 } { 4 } n ^ { 2 } ( n + 1 ) ^ { 2 }$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q4 [5]}}