Question 262821
(part a) If the first integer is x and the next consecutive integer is (x+1), then the sum of two consecutive integers can be expressed as
SUM = x + x + 1 = 2x + 1.
-------
(part b): 
CASE 1: Let the first number, x, be even. Then the next consecutive number, x+1, is odd.
Sum of x + x + 1 = even + odd = 2x + 1.
Notice that we cannot divide each term by 2. This means that an even + odd is odd.
CASE 2: Let the first number, x, be odd. Then the next consecutive number, x+1, is even.
Sum of x + x + 1 = odd + even = 2x + 1.
Notice that we cannot divide each term by 2. This means that an odd + even is odd.
---
So, the sum of 2 consecutive integers must always be odd.