Answer:
   λ₂ = 1,219 10⁻⁷ m
, λ₃ = 1.028 10⁻⁷ m
,   λ₄ = 0.9741 10⁻⁷ m
, λ₅ = 0.9510 10⁻⁷ m and  λ₆ = 0.9395 10⁻⁷ m
Explanation:
To calculate the lines of the hydrogen liman series, we can use the Bohr atom equation
            En = -13.606 / n²       [eV]
n       En
1       -13,606
2       -13.606 / 4 =    -3.4015
3       -13.606 / 9 =    -1.5118
4       -13.606 / 16 =  -0.8504
5       -13.606 / 25 = -0.5442
6       -13.606 / 36 = -0.3779
The lyma series are transitions where the state is fundamental (E1), let's calculate the first five transitions
State
 initial final energy
6           1      -0.3779 - (- 13.606) =  13.23 eV
5           1      -0.5442 - (- 13.606) =  13.06 eV
4           1      -0.8504- (-13.606) =   12.76 eV
3            1      -1.5118 - (- 13.606) =   12.09 eV
2            1      -3.4015 - (- 13.606) = 10.20 eV
Let's use the relationship between the speed of light and the wavelength and the frequency
       c = λ  f
       f = c / λ  
Planck's relationship for energy
      E = h f
      E = h c / λ
     λ = hc / E
We calculate for each energy
E = 10.20 eV
       λ  = 6.63 10⁻³⁴ 3 10⁸ / (10.20 1.6 10⁻¹⁹)
       λ  = 12.43 10⁻⁷ / 10.20
       λ₂ = 1,219 10⁻⁷ m
E = 12.09 eV
      λ₃ = 12.43 10⁻⁷ / 12.09
      λ₃ = 1.028 10⁻⁷ m
E = 12.76 eV
       λ₄ = 12.43 10⁻⁷ /12.76
       λ₄ = 0.9741 10⁻⁷ m
E = 13.06 ev
       λ₅=  12.43 10⁻⁷ /13.06
        λ₅ = 0.9510 10⁻⁷ m
E = 13.23 eV
       λ₆ = 12.43 10⁻⁷ / 13.23
       λ₆ = 0.9395 10⁻⁷ m