SPS SPS FM 2020 October — Question 4 5 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2020
SessionOctober
Marks5
TopicProof by induction
TypeProve summation formula
DifficultyStandard +0.3 This is a straightforward proof by induction with a simple summation formula. The base case is trivial, and the inductive step requires only basic algebraic manipulation of polynomials—no creative insight or complex factorization is needed. While it's a Further Maths question, it's a standard textbook exercise that's slightly easier than average A-level difficulty.
Spec4.01a Mathematical induction: construct proofs

Prove by induction that, for \(n \geq 1\), \(\sum_{r=1}^n r(3r + 1) = n(n + 1)^2\). [5]

Prove by induction that, for $n \geq 1$, $\sum_{r=1}^n r(3r + 1) = n(n + 1)^2$. [5]

\hfill \mbox{\textit{SPS SPS FM 2020 Q4 [5]}}