I'm trying to understand how Tsallis entropy generalizes Boltzmann-Gibbs entropy. The Tsallis Entropy wikipedia article says Tsallis entropy of a distribution $p_i$ is:
$$ s_q(p_i) = \frac{k}{q-1} \left( 1 - \sum_i p^q_i \right) ;~~~~~~~~ q > 0 $$
And that taking the limit as $q \rightarrow 1$ we recover the Botlzmann-Gibbs entropy:
$$ \lim_{q \rightarrow 1} S_q = S_{BG} = -k \sum_i p_i \ln p_i $$
How does one actually take this limit though? I'm not sure how to factor / deal with the $k/(q-1)$ term.
Thank you,