Question

What is the base case in the recursive summation function? sum(n) will calculate:

a) 1
b) 2
c) ... n
d) None of the above

Answer 1

The base case in a recursive summation function is typically when the function reaches the value sum(1) = 1, which prevents the recursion from continuing indefinitely.

Step-by-step explanation:

The base case in a recursive summation function is typically when the function reaches its smallest input value, typically sum(1), which would be equal to 1. This is because a sum from 1 to n includes the starting point, 1. In recursive functions, the base case is crucial as it provides the condition that stops the recursion from continuing indefinitely. For the function sum(n) that calculates the sum of numbers from 1 to n, the base case would be sum(1) = 1.

Here's a step-by-step explanation of how a recursive summation function might work:

1. If n is equal to 1, return 1. This is the base case.
2. If n is greater than 1, return n plus the result of sum(n-1), which calls the sum function with the next smaller number.
3. This process repeats until the base case is reached.