What is the way to this transition? $NM*log(1-\frac{U}{L(θ)}$$+o(\frac{log(NM)}{NM}$$))$=$(-\frac{U}{L(θ)}$$+o(log(NM))(1+o(1))$
N=M→∞
x=$-\frac{U}{L(θ)}$$+o(\frac{log(NM)}{NM}$)→0
I thought: For |x|<1 :
$\frac{1}{1+x}=1−x+x^2−x^3+$…⟹Integrate both sides elementwise $log(1+x)=x−\frac{x^2}{2}+\frac{x^3}{3}−\frac{x^4}{4}+…=x+O(x^2)=x(1+O(x))=x(1+o(1))$
But I'm not sure?