Sure, here are the Python programs for each of your requests:

1. Factorial of a number n:
```python
def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n-1)
```

2. Fibonacci numbers:
```python
def fibonacci(n):
if n

Question

Sure, here are the Python programs for each of your requests:

1. Factorial of a number n:
```python
def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
```

2. Fibonacci numbers:
```python
def fibonacci(n):
    if n <= 1:
        return n
    else:
        return(fibonacci(n-1) + fibonacci(n-2))
```

3. X^n:
```python
def power(x, n):
    if n == 0:
        return 1
    else:
        return x * power(x, n-1)
```

4. Consecutive sum of n numbers:
```python
def sum_n(n):
    if n == 0:
        return 0
    else:
        return n + sum_n(n-1)
```

5. Consecutive sum of n odd numbers:
```python
def sum_odd(n):
    if n == 0:
        return 0
    else:
        return (2*n-1) + sum_odd(n-1)
```

6. The sum of the following sequence: 1^2, 2^2, 3^2, ..., n^2:
```python
def sum_squares(n):
    if n == 0:
        return 0
    else:
        return n**2 + sum_squares(n-1)
```

7. Find GCD of two numbers:
```python
def gcd(a, b):
    if b == 0:
        return a
    else:
        return gcd(b, a % b)
```
Please note that these recursive functions are not the most efficient way to solve these problems, especially for large inputs, due to the overhead of function calls and the risk of exceeding the maximum recursion depth. Iterative solutions would be more efficient in such cases.

Knowee AI · Accepted Answer