Not really, because you've removed 'almost all' terms, but there are many ways to remove 'almost all' terms that do not result in a convergent series. For insta

Not really, because you've removed 'almost all' terms, but there are many ways to remove 'almost all' terms that do not result in a convergent series. For instance, you could remove 999 out of every 1000 terms. I'd say that counts as removing 'almost all' terms. Nevertheless, the resulting series does not converge, for the exact same reason that removing every other term doesn't work. The amount of terms that you remove has to increase faster than that.