The main scale of a vernier calliper has $n$ divisions/cm. $n$ divisions of the vernier scale coincide with $(n-1)$ divisions of the main scale. The least count of the vernier calliper is:

1. A
   $\frac{1}{n(n+1)}\text{cm}$
2. B
   $\frac{1}{(n+1)(n-1)}\text{cm}$
3. C
   $\frac{1}{n^2}\text{cm}$
4. D
   $\frac{1}{n}\text{cm}$