v₁ is the frequency of the series limit of Lyman series, v₂ is the frequency of the first line of Lyman series and v₃ is the frequency of the series limit of the Balmer series. Then

Step-by-step solution

For Lyman series v=R c [ 1 1^2 - 1 n^2 ] , where n=2,3,4, . For the series limit of Lyman series, n= For the first line of Lyman series, n=2 For Balmer series v=R c [ 1 2^2 - 1 n^2 ] , where n=3,4,5 . For the series limit of Balmer series, n= From eqns. (i), (ii) and (iii), we get v₁=v₂+v₃ or v₁-v₂=v₃ From eqns. (i), (ii) and (iii), we get v₁=v₂+v₃ or v₁-v₂=v₃