Divisibility by Induction
Show that is divisible by 2
If something is divisible by 2, it has 2 as a factor. In other words, it must be possible to write it as , where is an integer.
- Check that it is correct for the first value of by inserting the value into the expression :
- Assume that it’s correct for , now using the expression directly in the exercise, only switching with :
- You need to show that this is correct for , now using the expression directly in the exercise, only switching with . Don’t forget parentheses!
- You now begin the calculation part of your proof. It begins with the left-hand side of (5), and continues with the additional assumption (4). Look closely at what happens below! Finally, you’ll end up with what is on the right-hand side of the equality in (5).
Now using the assumption, gives the following: