GATE EC 2026 Set 1 Q26 — Complex Analysis

Consider the two series, $S_{A}$ and $S_{B}$, where

$$\begin{array}{l} S_{A}=\sum_{n=1}^{\infty} \frac{n^{2}}{2^{n}} \\ S_{B}=1+\frac{1}{2}+\frac{1}{8}+\frac{1}{16}+\frac{1}{64}+\frac{1}{128}+\frac{1}{512}+\cdots \end{array}$$
Which of the following statements is correct for the two given series?