I'm trying to find ways this simplify this formula and assuming numbers but that doesn't seem to help, the question is asking to prove or disprove:

$$ 3n(\log_{}n)^2 + 4n = \Omega (2n^2 \log_{}n +1) $$

I tried to assume $n_0$ as $1$ and $10$ to simplify it but that didn't help to find a positive constant $c$.

  • $\begingroup$ The claim is false. $\endgroup$ – Yuval Filmus Oct 12 at 6:34
  • $\begingroup$ How to simplify it so I don’t need to assume numbers $\endgroup$ – Xi N Oct 12 at 16:38
  • $\begingroup$ You can drop the low-order terms on both sides. $\endgroup$ – Yuval Filmus Oct 12 at 16:51
  • $\begingroup$ Does that work for proving things? $\endgroup$ – Xi N Oct 12 at 17:03
  • $\begingroup$ It works perfectly. Try to understand why, though. $\endgroup$ – Yuval Filmus Oct 12 at 17:31

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