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.
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:
chongli|8 months ago
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
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