Recursion and iteration are two great ways to solve problems, but they work a bit differently.

• Recursion: This is when a function (a piece of code) calls itself to solve a problem. Imagine a Russian nesting doll—each doll opens up to reveal another one inside. For example, if you want to find the factorial of a number ( n ) (which means multiplying all whole numbers from 1 to ( n )), you can use recursion like this:

[ \text{fact}(n) = n \times \text{fact}(n-1) \quad \text{with} \quad \text{fact}(0) = 1. ]

This means that to find the factorial of ( n ), you multiply ( n ) by the factorial of ( n-1 ). The base case is when ( n ) is 0, which equals 1.

• Iteration: This method uses loops, like a "while" loop or a "for" loop. It’s more straightforward and usually easier on memory. To find the factorial using iteration, it would look like this:

[ \text{fact}(n) = 1; \quad \text{for } i=1 \text{ to } n, \text{ multiply } \text{fact} \text{ by } i. ]

In simpler terms, you start with 1 and keep multiplying by each number up to ( n ).

In practice, recursion can be fancy and sometimes a bit confusing. On the other hand, iteration is often more direct and easier to understand!