Mathematical induction

Mathematical induction is like a game you play with numbers. First, you pick any number you want. Let's say you pick 5. Then, you check to see if the rule works for that number. For example, if the rule is "The sum of the first five numbers is 15," then you can check to see if 5+4+3+2+1 is equal to 15. If it is, then you have proven that the rule works for the number 5.

Now, in mathematical induction, you have to prove that the same rule works for any number you choose. To do this, you will start with a number and assume the rule works for that number. Then, you can prove that it works for the number after the one you picked. Let's assume the rule works for the number 5 again. This time, assume that the rule works for 5, then try to prove that it works for the number 6. To do this, you can use what you already know - the rule works for 5 - and add one more number, 6, to it. In this case, the rule would be "The sum of the first six numbers is 21." Adding 5+4+3+2+1+6 would give you 21, so you can use mathematical induction to prove that the rule works for 6 too!

This is the basics of mathematical induction - you start with a number and assume the rule works for it, then you prove that the same rule works for the number after it. You can keep repeating this until you have proven that the rule works for any number you choose.