> FWIW, if we replace both of these by writing them in exponential form,
> the limits are computed correctly:
>
> limit(%e^(n*log(7))/%e^(n*log(8)),n,inf) => 0 ...
> That might be a useful general heuristic to try.
%e^(n*log(7))/%e^(n*log(8)) simplifies to %E^(LOG(7)*n-LOG(8)*n),
which is why it works. If the original problem were (2^n+1)/(7^n+1),
it wouldn't work. And tlimit works correctly on 2^n/7^n precisely
because taylor converts to exponential form.
Sadly, tlimit( (2^n+1)/(7^n+1) , n, inf,5) exposes a *different* bug:
error: "two equal vars generated" -- I reported this as 1037916
ARGH!