Section 1.1: Utilizing the range() Function

When we think about finite sequences in Python, the range() function is often the first that comes to mind. It primarily serves to facilitate iteration over integer intervals. Here's a simple example of its use:

for i in range(10):

print(i)

Output: 0, 1, ..., 8, 9

You might have noticed that '10' is absent from the output. This is because range() halts before reaching the specified limit. If you want to include it, you can add an extra parameter like this:

for i in range(10, 14):

print(i)

Output: 10, 11, 12, 13

Additionally, we can create sequences that have specific steps using range():

for i in range(0, 20, 3):

print(i)

Output: 0, 3, 6, ..., 15, 18

Now, let’s explore how to construct nonlinear sequences.

Section 1.2: Fibonacci Sequence Generation

A classic example is generating the Fibonacci sequence, where each number is the sum of the two preceding ones. While a recursive approach may lead to inefficiencies, Python's generators provide a powerful alternative:

def fib():

a, b = 0, 1

yield a

while True:

a, b = b, a + b

yield b

fib_sequence = list(itertools.islice(fib(), 10))

print(fib_sequence)

Output: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

By using islice(), we can generate a sequence of a specified length efficiently.