Click and drag the given steps (in the right) to the corresponding step names (in the left) to show the inductive step to prove that P(n) is true. Step 1 If k + 1 is odd, then k is even, so 2 hat 0 was not part of the sum for k. Step 2 If k + 1 is even, then (k + 1)/2 is a positive integer, so by the inductive hypothesis (k + 1)/2 can be written as a sum of distinct powers of 2. Step 3 Increasing each exponent by 1 doubles the value and gives us the desired sum for k + 1. Step 4 Therefore the sum for k + 1 is the same as the sum for k with the extra term 2 hat 0 added. If k + 1 is odd, then k is even, so 2 hat 0 was not part of the sum for k. Increasing each exponent by 1 doubles the value and gives us the desired sum for k + 1. If k + 1 is even, then (k + 1)/2 is a positive integer, so by the inductive hypothesis (k + 1)/2 can be written as a sum of distinct powers of 2. If k + 1 is odd, then (k + 1)/2 is a positive integer, so by the inductive hypothesis (k + 1)/2 can be written as a sum of distinct powers of 2. If k + 1 is even, then k is even, so 2 hat 0 was not part of the sum for k. Therefore the sum for k + 1 is the same as the sum for k with the extra term 2 hat 0 added.