If 2 functions each big $\mathcal O$ of each other, then place them on the same level. $x^2 + x^3, 3^x, x!, x \log(x), x^2 + 2^x, 2^{x \log(x)}, \log(x^2), 6 \log(x), 2^x, x(1+2+\dots+x)$
My answer is:
$x(1+2+· · ·+x) = x(x(x+1))/2 = x(x^2+x)/2 = (x^3+x^2)/2$
The list is:
$x^2+x^3, \mathcal O((x^3+x^2)/2)$
$3^x, 2^x$
$x \log(x), \mathcal O(2^{x \log(x)})$
$6 \log(x), \log(x^2) = 2 \log x$
$x^2 + 2^x$
$x!$
Is this correct? Do I need to mention $\mathcal O(....)$ in my answer or can I remove the $\mathcal O$?
