Question 163
Which of the following expressions is larger: $A = \frac{1+a+a^2+\dots+a^{n-1}}{1+a+a^2+\dots+a^n}$,
$$
B = \frac{1+b+b^2+\dots+b^{n-1}}{1+b+b^2+\dots+b^n}, \text{ if } a \gt b \gt 0.
$$
$$
B = \frac{1+b+b^2+\dots+b^{n-1}}{1+b+b^2+\dots+b^n}, \text{ if } a \gt b \gt 0.
$$