Let v(1) be the frequency of the series ...

Let `v_(1)` be the frequency of the series limit of the Lyman series, `v_(2)` be the frequency of the first line of the Lyman series, and `v_(3)` be the frequency of the series limit of the Balmer series. Then

`vartheta_(1) vartheta_(2) = vartheta_(3)`

`vartheta_(2) - vartheta_(1) = vartheta_(3)`

`2 vartheta_(3) = vartheta_(1) + vartheta_(2)`

`vartheta_(1) + vartheta_(2) = vartheta_(3)`

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