### Q2. 25%, Checking mathematical series number

Fibonacci Sequence

Write a Python function named `check_mathematical_series` that takes a positive integer n as input and checks whether the given number belongs to any of the following important mathematical series: `Fibonacci sequence`, `Triangular sequence`, `Square sequence`.

The function should determine the series type and return a string indicating the result.

The possible return values are:

- "Fibonacci" if the number belongs to the Fibonacci sequence.
- "Triangular" if the number belongs to the Triangular sequence.
- "Square" if the number belongs to the Square sequence.
- "None" if the number does not belong to any of the above sequences.

For this question, consider the following definitions for the series:

1. Fibonacci sequence: A series of numbers in which each number (after the first two) is the sum of the two preceding ones. The sequence starts with 0 and 1. For example, the Fibonacci sequence begins as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, …

```python
def fibonacci_sequence(n):
    # Check if the input is valid
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    
    # Initialize the sequence with the first two numbers
    sequence = [0, 1]
    
    # Generate the Fibonacci sequence
    for i in range(2, n):
        next_num = sequence[-1] + sequence[-2]
        sequence.append(next_num)
    
    return sequence
```

2. Triangular sequence: A sequence of numbers in which each term represents the
total number of dots required to form a triangle with that many dots on each side.
The nth term of the triangular sequence is given by the formula (n * (n + 1)) / 2.
For example, the triangular sequence begins as follows: 1, 3, 6, 10, 15, …


```python
def triangular_sequence(n):
    # Check if the input is valid
    if n <= 0:
        return []
    
    # Initialize the sequence with the first number
    sequence = [1]
    
    # Generate the Triangular sequence
    for i in range(2, n+1):
        next_num = sequence[-1] + i
        sequence.append(next_num)
    
    return sequence
```


Square number sequence: A sequence of numbers that are the squares of
consecutive integers. For example, the square number sequence begins as follows:
1, 4, 9, 16, 25, 36, ...
Write the check_mathematical_series function and test it with the following values
of n:
    - 21
    - 9
    - 17
    - 10

```python
def square_number_sequence(n):
    # Check if the input is valid
    if n <= 0:
        return []
    
    # Initialize the sequence with the first number
    sequence = [1]
    
    # Generate the Triangular sequence
    for i in range(2, n+1):
        next_num = sequence[-1] + i
        sequence.append(next_num)
    
    return sequence
```

Print the result for each value of n, indicating the series types to which it belongs.

Using commas (,) if it belongs to more than 1 series.

"None" if it doesn't belong to any of the series.

Your function should have the following signature:

```python
def check_mathematical_series(n: int) -> str:
```

# Your code here

Example output:

```python
n = 21: Fibonacci, Triangular
n = 9: Square
n = 17: None
n = 10: Triangular
```

Note: You can assume that the given n will be a positive integer


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A:
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