How do I prove the following:
O(n^2 logn) is also O(n^3)?
$\displaystyle f(n)\in O(n^2 \log(n))$
means there exists a constant $\displaystyle k>0$ and an $\displaystyle N>0$ such that for all $\displaystyle n>N$:
$\displaystyle |f(n)|<k n^2 \log(n)$
Now for $\displaystyle n>0$ we have $\displaystyle n>\log(n)$ so for $\displaystyle n>N>0$:
$\displaystyle |f(n)|<k n^3$
etc.
CB