Provide an Appropriate Response $\frac { x } { 1 + x ^ { 2 } }$

question 95

Multiple Choice

Provide an appropriate response.
-Derive the series for $\frac { x } { 1 + x ^ { 2 } }$ for $x > 1$ by first writing $\frac { x } { 1 + x ^ { 2 } } = \frac { 1 } { x } \frac { 1 } { 1 + 1 / x ^ { 2 } }$ .

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { x ^ { 2 n } }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { x ^ { 2 n + 1 } }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { x ^ { 2 n + 1 } }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { x ^ { 2 n } }\)

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Definitions:

Pulse Pressure

The difference between systolic and diastolic blood pressure, indicating the force that the heart generates each time it contracts.

Systolic Pressure

The pressure in the arteries when the heart beats and fills them with blood, the higher number in a blood pressure reading.

Diastolic Pressure

The lowest pressure within the arteries, occurring between heartbeats when the heart is resting and refilling with blood.

Heart Sounds

Sounds produced by the closing of heart valves and the rushing of blood through the heart, typically heard as a "lub-dub" sound with a stethoscope.