MathCastle
Proof WritingChallengeInduction

Induction · Challenge problem

Induction proves 1⋅3+3⋅5+⋯+(2n−1)(2n+1)=n(4n2+an−1)31\cdot3 + 3\cdot5 + \cdots + (2n - 1)(2n + 1) = \dfrac{n(4n^2 + an - 1)}{3} for a certain constant aa. What is aa?