What is the sum of the products: 123; 234; ….; 505152?

Question

Answer 1

The expression can be written as $$\sum{n*(n+1)*(n+2)}$$ where 1 <= n <= 50

= $$\sum{n(n^2 + 3n + 2)} = \sum{n^3 + 3n^2 + 2n}$$ where 1 <= n <= 50

= $$(50*51/2)^2$$ + 3*50*51*101/6 + 2*50*51/2 = 1756950

Answer 2

The expression can be written as $$\sum{n*(n+1)*(n+2)}$$ where 1 <= n <= 50

= $$\sum{n(n^2 + 3n + 2)} = \sum{n^3 + 3n^2 + 2n}$$ where 1 <= n <= 50

= $$(50*51/2)^2$$ + 3*50*51*101/6 + 2*50*51/2 = 1756950

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What is the sum of the products: 1*2*3; 2*3*4; ….; 50*51*52?

What is the sum of the products: 123; 234; ….; 505152?