For Lyman series, $\mathrm{n}_1=1$
The wave number of lowest transition associated with Lyman series corresponds to the transition from $n=2$ to $n=1$.
Therefore, $\mathrm{n}_2=2$
$\begin{aligned}
\therefore \quad \bar{v} & =\mathrm{R}_{\mathrm{H}}\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right] \mathrm{cm}^{-1} \\
& =\mathrm{R}_{\mathrm{H}}\left[\frac{1}{1^2}-\frac{1}{2^2}\right] \mathrm{cm}^{-1}
\end{aligned}$
$=\mathrm{R}_{\mathrm{H}}\left[1-\frac{1}{4}\right] \mathrm{cm}^{-1}=\mathrm{R}_{\mathrm{H}}\left[\frac{3}{4}\right] \mathrm{cm}^{-1}$