Let F(z)=\frac{z+i}{z-i} for all complex numbers z \neq i, and let z_{n}=F\left(z_{n-1}\right) for all positive integers n. Given that z_{0}=\frac{1}{137}+i and z_{2002}=a+b i, where a and b are real numbers, find a+b.
Let F(z)=\frac{z+i}{z-i} for all complex numbers z \neq i, and let z_{n}=F\left(z_{n-1}\right) for all positive integers n. Given that z_{0}=\frac{1}{137}+i and z_{2002}=a+b i, where a and b are real numbers, find a+b.