Parity (Even/Odd) Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
mediumProve that the sum of any two consecutive integers is always odd.
Solution
- 1 Let the two consecutive integers be and .
- 2 Their sum: .
- 3 is always even (divisible by ), so is always odd.
- 4 Therefore the sum of any two consecutive integers is odd.
Answer
Sum , which is always odd.
Using algebra with a general integer lets us prove the parity result for all possible pairs at once. The form is the definition of an odd number: any number of the form for integer is odd.
About Parity (Even/Odd)
The classification of integers as even (evenly divisible by 2, with no remainder) or odd (not divisible by 2).
Learn more about Parity (Even/Odd) →More Parity (Even/Odd) Examples
Example 1 easy
Without fully computing, determine the parity (odd or even) of [formula] and of [formula].
Example 3 mediumProve that the sum of two odd numbers is always even.
Example 4 easyClassify each as odd or even without fully computing: (a) [formula], (b) [formula], (c) [formula].
Example 5 mediumIn a group of [formula] people, each person shakes hands with every other person exactly once. Is th