Can you tell me if it's ok to manipulate the limit of a summation in this way please?
$$ \sum \limits _{l = k_o}^{+ \infty} q^{l - k_0} = \sum \limits _{l - k_0 = 0}^{+ \infty} q^{l - k_0} $$
Are there rules about the possible operations I can perform on the superior and inferior limits?
I see what you are doing, but this is unconventional to have an equation in the lower index of the summation. Less confusing variant involves the change of variable: $$ \sum \limits _{l = k_0}^{+ \infty} q^{l - k_0} \stackrel{}{=} \sum \limits _{n = 0}^{+ \infty} q^{n} $$
If you are afraid the reader cannot follow, you can add substituting summation index $n=l-k_0$ somewhere in the text