Question

Show algebraically that the sum of two consecutive numbers is always odd.

Note: Let n stand for any integer in your working.

Answer 1

See below.

Explanation:

We are asked to prove that n + (n+1) will always result in an odd number. Let's assume n is an even number. (n+1) must be an odd number. Let's rewrite the expression:

n + n + 1 is odd.

If n is even, n+n will also be even. Add 1 to n+n will make it odd.

If n were odd, n+n will be even. Add 1 to an even number will make it odd.