Total lines from level n to all lower levels: n$\frac{n-1}{2}$. Lines in a specific series (to level n1): n - n1. From n=4: total = 4$\frac{3}{2}$ = 6 lines. Lyman: 4-1=3, Balmer: 4-2=2, Paschen: 4-3=1. Check: 3+2+1=6. Wavelength calculation: 1/lambda = $RZ^2$(1/$n1^2$ - 1/$n2^2$). Longest wavelength in series = smallest energy transition (n2 = n1+1). Shortest wavelength (series limit) = largest energy transition (n2 = infinity). For the Balmer series limit: 1/lambda = R$\frac{1}{4}$ => lambda = 4/R = 364.7 nm. First Balmer line (H-alpha): lambda = 656 nm. Energy gap decreases as n increases (levels get closer together).