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rak1507 | 8 months ago

Why not? All that is really required is knowing 1/(1-x) = 1+x+x^2+... and a bit of algebraic manipulation.

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chongli|8 months ago

And the idea of a formal power series. And integer compositions. And combinatorial enumeration (counting sets in different ways for a proof). And a bit of set theory (cardinality of sets).

There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.

rak1507|8 months ago

You definitely don't need to know any of that background to be able to arrive at the answer. To fully understand everything maybe, but all it takes is:

a = x^1 + x^4 + x^7 + ... = x(1 + x^3 + x^6 + ...) = x/(1-x^3)

a + a^3 + a^5 + ... = a(1 + a^2 + a^4 + ...) = a/(1-a^2)

Substitute + simplify. I don't think this is beyond a (fairly smart) elementary school student.

redczar|8 months ago

You obviously have not taught mathematics to high school students.