Final answer:
The number of times "Hello" is printed by the loop system is the nth triangular number, calculated as (n(n+1))/2, which is the sum of 1+2+3+...+n, representing the total prints for each outer loop iteration.
Step-by-step explanation:
You're asking how many times "Hello" is printed by the given system of loops. Let's break it down:
The outer loop runs from k = 1 to n. Each time this loop runs, "Hello" is printed once. But then, the inner loop runs, printing "Hello" another k times. So, for k = 1, "Hello" is printed 1 extra time (once by the outer loop and once by the inner), for k = 2, it's printed 3 times in total (once by the outer loop and twice by the inner), and so on.
When you add these up across all iterations, you get a series that sums to the nth triangular number: 1 + 2 + 3 + ... + n, which equals to (n(n + 1)) / 2. That's because each successive term represents the total count of "Hello" for that iteration of the outer loop.
Therefore, the correct answer is (n (n+1)) / 2, which is option a.