Suppose $$a_{1} = \dfrac{1}{2-\frac{1}{2}}, a_{2} = \dfrac{2}{3-\frac{1}{3}},a_{3} = \dfrac{3}{4-\frac{1}{4}},a_{4} = \dfrac{4}{5-\frac{1}{5}},a_{5} = \dfrac{5}{6-\frac{1}{6}}.$$ a) Find an explicit formula for $a_{n}$: .

b) Determine whether the sequence is convergent or divergent: .
(Enter "convergent" or "divergent" as appropriate.)

c) If it converges, find $\lim_{n\rightarrow\infty}a_{n} =$ .