Which of the Following Is the Power Series Centered At a =

question 165

Multiple Choice

Which of the following is the power series centered at $a = 0$ for $f ( x ) = \frac { 1 } { 1 + 4 x }$ ?
1) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } 4 ^ { n } x ^ { n }$ 2) $\sum _ { n = 0 } ^ { \infty } 4 ^ { n } x ^ { n }$ 3) $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 4 ^ { n } } x ^ { n }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

---

Definitions:

Depressant

A substance that reduces the functioning of the nervous system, often used to decrease anxiety and induce sleep.

Narcotic

A class of substances that relieve pain and induce a state of sleep or stupor; often associated with opioids, which can be both legal medications and illicit drugs.

Barbiturates

A class of drugs that are used as sedatives and hypnotics, which can depress the central nervous system.

Drug Interaction

A modification in the effect of a drug when it is taken in combination with another drug, leading to increased efficacy, reduced effectiveness, or adverse side effects.