So, write it out and ponder it...

You may be expected to 1) Recognize the structure of the Geometric Series and 2) Know the formula for the sum.

Note: The question is a little funny. I don't really like the phrase "maximum height that the tree will reach". I would prefer a limit sort of phrase, maybe something like "What height will the tree approach?" or "What is the minimum height the tree will NOT exceed?" It is a tough concept to get exactly right. Maybe the original question is okay for now.