If the power series
$$ sum_{n=1}^{infty} c_n z^n$$
converges and has radius of convergence $$r=1$$ (this is a complex power series) and if $$ T$$ is a strictly increasing map of natural numbers to natural numbers (T_n being hence a strictly increasing sequence of natural numbers) find the radius convergence of

$$ sum_{n=1}^{infty} c_n z^{T_n}$$

I have tried to think of particular sequences, such as

$$ T_n = n^2 $$

or similar, however, no clear idea coming to my mind how to proceed even with that. I also focused on the nature of the sequence, but not coming to any idea.
Is there any particular theorem that can be applied here?