4 ms·

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

• chongli 1y 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 1y 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.
    • chongli 1y ago
      The question doesn’t ask for an answer, it asks for a proof. You can’t just write a bunch of algebra and call it a day. You have to justify all of your arguments.
      • rak1507 1y ago
        There aren't really any complicated arguments being made, so I don't think a proof would be that involved.
• redczar 1y ago
  You obviously have not taught mathematics to high school students.