Sure, here is a Python function that calculates the nth triangular number using recursion: ```python def triangular(n): if n 1 T(n) = n for n

Question

Sure, here is a Python function that calculates the nth triangular number using recursion:

```python
def triangular(n):
    if n <= 1:
        return n
    else:
        return n + triangular(n-1)
```

This function works by checking if `n` is less than or equal to 1. If it is, it returns `n` (since the first triangular number is 1). If `n` is greater than 1, it adds `n` to the result of the function called with `n-1`. This is the recursive step, where the function calls itself.

The recurrence relation for this function is:

T(n) = n + T(n-1) for n > 1
T(n) = n for n <= 1

This relation expresses the time complexity of the function. It says that to compute T(n), you add n to the result of T(n-1). This continues until n is less than or equal to 1, at which point T(n) is simply n.

Knowee AI · Accepted Answer

Sure, here is a Python function that calculates the nth triangular number using recursion:

```python
def triangular(n):
    if n <= 1:
        return n
    else:
        return n + triangular(n-1)
```

This function works by checking if `n` is less than or equal to 1. If it is, it returns `n` (since the first triangular number is 1). If `n` is greater than 1, it adds `n` to the result of the function called with `n-1`. This is the recursive step, where the function calls itself.

The recurrence relation for this function is:

T(n) = n + T(n-1) for n > 1
T(n) = n for n <= 1

This relation expresses the time complexity of the function. It says that to compute T(n), you add n to the result of T(n-1). This continues until n is less than or equal to 1, at which point T(n) is simply n.

c). Write a recursive function to find the nth “Triangular” number and write therecurrence relation for the function. [20%](Hint: A triangular number is the sum of itself and all other smaller numbers. Forexample, the triangular number of 4 is, 4+3+2+1 = 10.)

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