Question: 1. Suppose G is connected and k-regular and has no Eulerian circuit. Prove that if G¯ is connected, then G¯ has an Eulerian circuit.
2. Consider an = 2n - 1 and form the new sequence sn = a1 + a2 + ··· + an. Fill in the blanks in this table:
What is the relationship between the bottom two rows? Use this relationship to write a recurrence relation for sn.