The series in the he spectrum that corresponds to the set of transitions where the electron falls from a higher level to the nf = 4 state is called the pickering series, an important series in solar astronomy. calculate the pickering series wavelength associated with the excited state ni = 6.

Ok so here is the thing. It is necessary to introduce the atomic number Z into the following equation and the reason for that is that we are not working here with hydrogen (H). It will go like this:  
E=(2.18×10^-18 J)(Z^2 )|1/(ni^2 )-1/(nf^2 )| 
E=(2.18×10^-18 J)(2^2 )|1/(6 ^2 )-1/(4 ^2 )|=3.02798×10^-19 J 

After that we need to plug the E value calculated into the equation. Remember that the wavelength is always positive:

E=hc/λ3.02798×10^-19 J=hc/λλ=6.56×10^-7 m 

so 6.56×10^-7 m or better written 656 nm is in the visible spectrum