Answer
$S=\dfrac{-1}{2},\dfrac{-1}{4}, \dfrac{-3}{8}, \dfrac{-5}{16}, \dfrac{-11}{32}$
Work Step by Step
Our aim is compute the first five partial sums for the given sequence.
$S_1=\dfrac{-1}{2}; S_2=\dfrac{-1}{2}+\dfrac{1}{4}=\dfrac{-1}{4}; S_3=\dfrac{-1}{2}+\dfrac{1}{4}-\dfrac{1}{8}=\dfrac{-3}{8}; S_4=\dfrac{-1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}=\dfrac{-5}{16}; S_5=\dfrac{-1}{2}+\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{16}-\dfrac{1}{32}=\dfrac{-11}{32}$
Thus, our partial sums are:
$S=\dfrac{-1}{2},\dfrac{-1}{4}, \dfrac{-3}{8}, \dfrac{-5}{16}, \dfrac{-11}{32}$
