Suppose g is connected and k-regular and has no eulerian

Question

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 a_n = 2ⁿ - 1 and form the new sequence s_n = a₁ + a₂ + ··· + a_n. 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 s_n.