quiz

def triangle(num):

    if num == 1:

        return num

    return num + triangle(num - 1)

Your function triangle(num) is a recursive way to calculate the triangular number — the sum of all integers from 1 up to num.

How it works

• Base case: If num == 1, it returns 1.

• Recursive case: Otherwise, it returns num + triangle(num - 1), which keeps calling itself until it reaches 1.

So for triangle(4):

• 4 + triangle(3)

• 4 + (3 + triangle(2))

• 4 + (3 + (2 + triangle(1)))

• 4 + 3 + 2 + 1 = 10

Key points

• It computes the sum $1+2+\cdots +n$.

• This is known as the n-th triangular number.

• Formula: $\frac{n(n+1)}{2}$
  

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def square(num):

    return triangle(num-1) + triangle(num)

Explanation

• triangle(n) gives the sum of integers from 1 to n. Example: triangle(4) = 1+2+3+4 = 10.

• In your square(num) function, you’re adding:

• triangle(num-1) → sum of numbers up to num-1

• triangle(num) → sum of numbers up to num

If num = 4

square(4) = 16

triangle(3) + tringle(4) = 6 + 10 = 16

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