# Python Project: Fibonacci

## Project Description

The Fibonacci sequence is as follows.

`0 1 1 2 3 5 8 13 21 34 ...` (continues)

It is generated as follows.

The next number is generated by adding the two last numbers.

```0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
...
```

Write a program that prints the Fibonacci sequence.

You will do it in two ways in this project.

## Step 1 The direct way

How to solve this?

Well, the first thought is to make it in an iterative way.

```def fib(n):
if n <= 1:
return n

i = 0
j = 1

for _ in range(n):
i, j = j, i + j

return i
```

You try to follow how the sequence is calculated and this can be done, but seems easy to get lost in the code.

To generate the sequence you can run this code.

```for i in range(10):
print(fib(i))
```

## Step 2 The simple way (recursive)

The first time you see recursion, it might not be easy to understand.

But after inspecting the following code, you might find it easier to write and follow.

```def fib(n):
if n <= 1:
return n
return fib(n - 1) + fib(n - 2)
```

This actually generates the same sequence.

The code is actually writing the exact formula for generating it.

You can get the sequence as follows.

```for i in range(10):
print(fib(i))
```

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