Consider the follwoing two elerctronic transition possibilites in a hydrogen atom as pictured below :

(1) The electron drops from third Bohr's orbit to second Bohr's obit followed with the next transition from second to first Bohr's orbit .
(2) The electron drops from third Bohr's orbit to first Bohr's orbit directly .
Show that :
(a) The sum of the enrgies for the transitions ` n=3` to ` n=2` and ` n=2` to ` n=1` is equal to the energy of transiton for ` n=3` to ` n=1` .
(b) Are wavelengths and frequencies of the emitted spectrum also additive in the same way as their energies are ?