so that the frequency of the first line in the Lyman series is equal to the difference between the limiting frequences of the Lyman and balmer series
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The 'series limit' refers to the 'shortest wavelength' (corresponding to the maximum photon energy). Here, k is a constant. Thus, the difference in the frequencies of the series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series.
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