Question 49
For the infinite series $$
\begin{aligned} &1-\dfrac12-\dfrac14+\dfrac18\\ &{}-\dfrac1{16}-\dfrac1{32}+\dfrac1{64}\\ &{}-\dfrac1{128}-\cdots, \end{aligned}
$$ let $S$ be the (limiting) sum. Then $S$ equals:
\begin{aligned} &1-\dfrac12-\dfrac14+\dfrac18\\ &{}-\dfrac1{16}-\dfrac1{32}+\dfrac1{64}\\ &{}-\dfrac1{128}-\cdots, \end{aligned}
$$ let $S$ be the (limiting) sum. Then $S$ equals: