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Interesting I want to think about this, don't reveal the answer or anything!

It seems like it's related to counting in base 2.

We can lower the bound to a finite number. By separating the two terms on top, we can see that these terms will be 0.
\[\frac{n}{2^{i+1}} < \frac{1}{2}\]
\[\log_2(n)*
*

that animation looks interesting, this is from bs grewal's advanced mathematics practice problems