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Single Variable Calculus

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Moderate

Alternating Sequences, Fractions

SVCALC-VYMUVL

Which of the following expressions describes the sequence:

$$\frac{1}{2}, -\frac{3}{4}, \frac{7}{8}, -\frac{15}{16},\frac{31}{32},\frac{63}{64},\ldots\;$$

A

$ \ { a \ _n}\_{n=1}^\infty=(-1)^{n-1}\frac{2^n-1}{2^n}$

B

$\{a\_n\}\_{n=1}^\infty=(-1)^{n}\frac{2^n-1}{2^n}$

C

$\{a\_n\}\_{n=1}^\infty=(-1)^{n-1}\frac{2^{n-1}}{2^n}$

D

$\{a\_n\}\_{n=1}^\infty=(-1)^{n}\frac{2^{n-1}}{2^n}$

E

$\{a\_n\}\_{n=1}^\infty=(-1)^{n}\frac{2^{n}}{2^{n+1}}$