Evaluate (\(\frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + ...) -1\)
A
2/3
B
zero
C
-2/3
D
-1
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
S\(_{\infty}\) = \(\frac{\text{a}}{(1-r)}\), where a = \(\frac{1}{2}\), r = -\(\frac{1}{2}\).
S\(_{\infty}\) = \(\frac{\frac{1}{2}}{1 - \frac{-1}{2}}\) = \(\frac{\frac{1}{2}}{\frac{3}{2}}\) = \(\frac{1}{2}\) x \(\frac{2}{3}\)
\(\frac{1}{3}\) - 1 = -\(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #720)