Answer
See below.
Work Step by Step
An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $|0.75|\lt1$.
Hence the sum: $\dfrac{1}{1-0.75}=4$
This means that the total sum of the triangles' area has an upper bound of $4$ square units.
