Induction on summations

For each of the sequences below, the corresponding activity will lead you to explore the nature of induction proofs as applied to closed formulas for summations.

• Summation 1. 1 + 2 + 3 + ··· + n = (n² + n)/2
• Summation 2. 2 + 4 + 6 + ··· + 2n = n² + n
• Summation 3. 1 + 3 + 5 + ··· + (2n - 1) = n²