1 3 5 7 2n 1 n 2 July 8, 2019 16 32 64 128 1 3 5 7 ⋯ 2n 1 n 2 1 3 5 7 9 2n 1 n 2 Prove by induction that 1 3 5 7 ⋯ 2n 1 n 2 1 + 3 + 5 + · · · + (2n − 1) = n 2