> In this particular case look at the difference between (n+1)^3 - (n+1)
> and n^3 - n. The difference has a factor 3, so "and so on" actually
But why would anyone use induction here? After all, whatever the positive number n may be, n^3 - n = (n - 1) n (n + 1) is the product of three consecutive whole numbers, and so has a multiple of 3 as a factor.
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