This problem quite similar to SMO Open 2024 review problem 1 which did NOT use summation(sigma) notation in the directions. Which property/axiom of addition allows us to split sigma of the sum into two separate summation symbols? Answer: The commutative property! Double summation compact way to avoid the clutter and ambiguity of long ellipsis filled expressions.
The sum of the first n square integers closed form formula was needed.
Also one can do this by n(n+1)(n+2)/6 which is proven by induction in many Discrete math courses.
Saturn, at stack exchange, December 2013, proved by induction that n(n+1)(n+2) is divisible by 6, BUT just checking the possible remainders upon division by 6, 0,1,2,3,4,5 shows that n(n+1)(n+2==0 modulo 6 and is better and more intuitive proof than tedious induction way
Негізгі бет Find the Sum of the first 60 Triangular Numbers. Similar SMO Open 2021 Review problem 1
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