$\text { Write an equivalent series of the series } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { n } } { n ! } \text { with the index of summation }$

question 143

Multiple Choice

$\text { Write an equivalent series of the series } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { n } } { n ! } \text { with the index of summation }$ beginning at $n = 5$ .

• A) \(\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n - 5 } } { ( n - 5 ) ! }\)
• B) \(\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n - 5 } } { n ! }\)
• C)\(\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n + 5 } } { n ! }\)
• D)\(\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n + 5 } } { ( n + 5 ) ! }\)
• E)\(\sum _ { n = 5 } ^ { \infty } \frac { x ^ { n } } { ( n - 5 ) ! }\)

---

Definitions:

Obstructive Sleep Apnea

A sleep disorder characterized by pauses in breathing or periods of shallow breathing during sleep due to airway blockage.

Bruxism

A condition where an individual grinds, gnashes, or clenches their teeth, often unconsciously, especially during sleep.

Daytime Fatigue

A condition characterized by persistent tiredness and lack of energy during the daytime, not directly linked to lack of sleep.

REM Rebound

The increase in the frequency and intensity of REM (Rapid Eye Movement) sleep following a period of REM sleep deprivation.