Mathematics - Sequence & Series Question with Solution | TestHub

$B_n=1-A_n>A_n\Rightarrow A_n<\frac{1}{2}$ Now, $A_n=\frac{\frac{3}{4}\left(1-{\left(-\frac{3}{4}\right)}^n\right)}{1+\frac{3}{4}}<\frac{1}{2}\Rightarrow \left(-\frac{3}{4}\right)>-\frac{1}{6}$ Obviously, it is true for all even values of $n$. But, for $$\begin{array}{rlrl}n& =1,& \frac{3}{4}& <\frac{1}{6}\\ n& =3,& \frac{27}{64}& <\frac{1}{6}\\ n& =5,& \frac{243}{1024}& >\frac{1}{6}\end{array}$$ which is true for $n=7$. Obviously, $n_0=7$