Final answer:
This algorithm calculates the sum of squares of the first n positive integers by adding each term i*i to a running total S iteratively, rather than using a simplified formula. It exemplifies a straightforward computational approach to summing a series without applying series expansions or the binomial theorem.
Step-by-step explanation:
The algorithm in question computes the sum of the squares of the first n positive integers. In other words, it calculates S as the sum of the series 12 + 22 + 32 + ... + n2. The expression S = S + i*i within the loop indicates that each term i2 is being added to the running total S.
By analyzing this algorithm with the concept of series expansions, particularly the binomial theorem, we can simplify the sum of squares series into a formula. However, the algorithm does not directly make use of any simplified formula; it calculates the total by iteratively adding each square.
If one were to derive a formula for the sum of squares, it would be found using the mathematical principle that the sum of the first n squares is n(n + 1)(2n + 1) / 6, but this specific formula is not what the algorithm is using to compute its result.The given algorithm computes the sum of the products of integers from 1 to n multiplied by themselves. It starts with an initial value of S = 0 and for each i from 1 to n, it calculates S = S + i*i. Finally, it returns the value of S.