Recursion is a fun idea, kind of like those Russian nesting dolls, where each doll has a smaller one inside. In computer science, recursion means a function calls itself to help solve smaller parts of a problem. Let’s look at some real-life examples to understand it better!

Example 1: Factorial

Calculating the factorial of a number, which is written as $n!$, is a common example. The factorial of a number is defined like this:

• $n! = n \times (n-1)!$ for $n > 0$
• $0! = 1$

This means if you want to find $5!$, you break it down like this: $5 \times 4!$. You keep going until you get to $0!$.

Example 2: Fibonacci Sequence

The Fibonacci sequence starts with $0$ and $1$. Each number after that is the sum of the two numbers before it:

• $F(n) = F(n-1) + F(n-2)$ for $n > 1$

So, to figure out $F(5)$, you would first find $F(4)$ and $F(3)$, and keep going until you reach the starting numbers.

These examples show how recursion makes solving complicated problems easier by breaking them down into smaller, simpler parts!