Originally Posted by

**TKHunny** So, write it out and ponder it...

$\displaystyle 2 + 1 + 4/5 + (4/5)^{2} + (4/5)^{3} + ... = 2 + \left(\frac{1}{1-\frac{4}{5}}\right)$

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.