But how does Coulomb's law explain this? because according to Coulomb's law (F=q1q2/r^2),smaller r give higher force. for n=1, it has the smallest r with respect to the nucleus. thus n=1 should have the highest attractive force right? but it has the lowest energy.how does those two go together?
There are a couple of things that might help you:
First, Coulomb's law tells us about the force between two charged particles. It doesn't tell us anything at all about energy (at least not directly). Also note that the negative sign for force is just telling you about the direction of the force, in this case it's radially inward, where you have put the center of your coordinate system on the nucleus.
Second, a better way is to look instead at the Coulomb potential between the electron and proton (U = -k * e^2/r). If you look at the energy levels for the electron, higher and higher values for n will yield energies which are closer and closer to zero. This makes sense because we've defined the reference point to be when the proton and electron are infinitely far away.
So, as you bring two oppositely charged particles together, the magnitude of the attractive force they feel becomes larger (remember the negative sign tells you the direction) and their energy becomes more and more negative. This should also make sense since, to separate them, you would have to do positive work on the system to pull them apart.
Hopefully this has answered your question. Let me add a little layer of complexity on here, although if it's not something your classes covered, feel free to ignore it. Classically speaking, we would expect the proton and the electron to accelerate towards each other and collide with one another, but this doesn't happen. The reason for this is due to the Heisenberg uncertainty principle - there is always a certain degree of ambiguity to the electrons position and momentum and therefore, at such small scales, the electron will never be
exactly on top of the proton. Instead, it happens to be in some vicinity around the nucleus which is described by the atomic orbitals that you're no doubt familiar with and has the energies that are predicted by the equation involving n that you've seen.
A more complicated description is that the electron orbitals are the eigenvectors of the time-independent Hamiltonian for a spherically symmetric Coulomb potential and the energies are the eigenvalues of the Hamiltonian. This is a much more powerful approach, but most likely beyond the scope of first and second year courses, unless your chemistry class happened to delve into quantum mechanics.
