N is a positive intiger. Explain why 2n+1 must be an odd number.

Because the number would be multiplied by an even number, which is 2. If the number (odd or even) is multiplied by two, then the result would be an even number.

Proof:

2 (1) = 2

2 (6) = 12

2 (7) = 14

2 (3) = 6

The number would then be added by an odd number, which is 1. If an even number is added with an odd number, then the result would be an odd number.

Proof:

2 + 1 = 3

12 + 1 = 13

14 + 1 = 15

6 + 1 = 7