I could not find a Desmos teacher activity exploration for series, so I made my own. Everything is better with Desmos!
This activity works best if students are already familiar with geometric sequences and series. They are really just exploring convergent and divergent. I instruct them to look up the words convergent and divergent in the dictionary. I thought knowing these definitions would help it make sense. I also included a geometric sequence and series link from Math Is Fun at the end.