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For Lyman series $v=Rc\left[\frac{1}{1^2}-\frac{1}{n^2}\right]$, where $n=2,3,4,\dots \dots$. For the series limit of Lyman series, $n=\infty$
For the first line of Lyman series, $n=2$
For Balmer series $v=Rc\left[\frac{1}{2^2}-\frac{1}{n^2}\right]$, where $n=3,4,5\dots$. For the series limit of Balmer series, $n=\infty$
From eqns. (i), (ii) and (iii), we get $v_1=v_2+v_3$ or $v_1-v_2=v_3$ From eqns. (i), (ii) and (iii), we get $v_1=v_2+v_3$ or $v_1-v_2=v_3$