(4) Let the area of the equilateral triangle $\triangle_{1}$ be $S_{1}$, construct the incircle of $\triangle_{1}$, then construct the inscribed equilateral triangle of the incircle, denoted as $\triangle_{2}$, with area $S_{2}$, and so on, creating a series of equilateral triangles $\triangle_{3}$, $\triangle_{1}, \cdots$, with corresponding areas $S_{3}, S_{4}, \cdots$, given $S_{1}=1, T_{n}=S_{1}+S_{2}+\cdots+$ $S_{n}$, then $\lim _{n \rightarrow+\infty} T_{n}=(\quad)$.
(A) $\frac{6}{5}$
(B) $\frac{4}{3}$
(C) $\frac{3}{2}$
(D) 2
(4) B Hint: This series of triangles are similar triangles, with a similarity ratio of $\frac{1}{2}$, so the areas form a geometric sequence with a common ratio of $\frac{1}{4}$. Thus, $T_{n}=\frac{1-\left(\frac{1}{4}\right)^{n}}{1-\frac{1}{4}}$, hence $\lim _{n \rightarrow+\infty} T_{n}=\frac{4}{3}$.