Step 1: Understand the structure of amines.
Amines are organic compounds that contain nitrogen (N) attached to carbon atoms. The general formula for primary amines is C$_n$H$_{2n+1}$N, where "n" is the number of carbon atoms in the molecule.
Step 2: Analyze the options.
- C$_n$H$_{2n+1}$N (Option A) is the correct formula for primary amines.
- C$_n$H$_{2n+2}$N (Option B) would suggest an additional hydrogen, which is not typical for amines.
- C$_n$H$_{2n+3}$N (Option C) is incorrect for primary amines.
- C$_n$H$_{2n}$N (Option D) is also incorrect as it does not account for the extra hydrogen in primary amines.
Step 3: Apply to the options.
The correct formula for primary amines is (A) C$_n$H$_{2n+1}$N.
Final Answer:
\[
\boxed{\text{C}_n\text{H}_{2n+1}\text{N}}
\]