Hello! Today we're going to learn about recursion, which is like a magic trick in programming. Imagine you have boxes inside boxes inside boxes, and each box contains a smaller version of itself. This is exactly how recursion works - a function that calls itself with a smaller problem until it reaches the simplest case.
Now let's see recursion in action with a simple countdown function. We start with the number 5, and each time we call the function again with a smaller number. Watch as we count down: 5, 4, 3, 2, 1. When we reach 1, that's our base case - the point where we stop calling ourselves and start returning back up.
Let's explore factorial, which is a classic example of recursion. To calculate 5 factorial, we need 5 times 4 factorial. To get 4 factorial, we need 4 times 3 factorial, and so on. This continues until we reach our base case: 1 factorial equals 1. Then we work backwards, multiplying each result to get our final answer of 120.
The Fibonacci sequence is a famous mathematical pattern that shows recursion beautifully. Each Fibonacci number is calculated by adding the two previous numbers together. We start with our base cases: the first and second Fibonacci numbers are both 1. Then each new number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, and so on.