Question: 3^n-1 is a multiple of 2?
Answer: 3n−1 is a multiple of 2 for n = 1, 2, ... The first part (2×3k) is certain to be a multiple of 2 and the second part (3k−1) is also true as our previous assumption. Hence, 3k+1–1 is a multiple of 2. So, it is proved that 3n–1 is a multiple of 2.