A factory makes custom sports cars at an increasing rate. In the first month, only one car is made, in the second month, two cars are made, and so on, with $n$ cars made in the $nth$ month.
- Set up a recurrence relation for the number of cars produced in the first $n$ months by this factory.
- How many cars are produced in the first year?
- Find an explicit formula for the number of cars produced in the first $n$ months by this factory
