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*= (*n*^{2}+*n*)/2 - Summation
2. 2 + 4 + 6 + ··· + 2
*n*=*n*^{2}+*n* - Summation
3. 1 + 3 + 5 + ··· + (2
*n*- 1) =*n*^{2}