Question 10
Given that
$$\frac AB=2-\cfrac1{2-\cfrac1{2-\cfrac1{\ddots-\cfrac1{2-\frac{2016}{2017}}}}}.$$
has 2017 layers as shown, where $A,B$ are positive integers, find $A+B$. Note that
$$2-\cfrac1{2-\frac{2016}{2017}}$$
is the first layer.
Source note: no condition that $A/B$ is in lowest terms is printed; this affects uniqueness.
$$\frac AB=2-\cfrac1{2-\cfrac1{2-\cfrac1{\ddots-\cfrac1{2-\frac{2016}{2017}}}}}.$$
has 2017 layers as shown, where $A,B$ are positive integers, find $A+B$. Note that
$$2-\cfrac1{2-\frac{2016}{2017}}$$
is the first layer.
Source note: no condition that $A/B$ is in lowest terms is printed; this affects uniqueness.