Determine the Number of Terms Sufficient to Obtain the Sum $\sum _ { n = 0 } ^ { \infty } \frac { ( - 5 ) ^ { n + 3 } } { ( n + 1 ) ! }$

question 21

Multiple Choice

Determine the number of terms sufficient to obtain the sum of the series accurate to three decimal places. $\sum _ { n = 0 } ^ { \infty } \frac { ( - 5 ) ^ { n + 3 } } { ( n + 1 ) ! }$

• A) 19
• B) 22
• C) 20
• D) 21

---

Definitions:

Bacterial Decomposition

The process by which bacteria break down organic material, such as dead organisms or waste, into simpler substances.

Organic Nitrogen

Nitrogen that is incorporated into organic compounds, a vital element for life processes within organisms.

Ammonia

A colorless gas with a pungent smell, NH3, used as a nitrogen source in fertilizers and as a cleaning agent.

Solar Radiation

The electromagnetic energy emitted by the sun, which reaches the earth and is a key factor in climate and weather patterns, as well as photosynthesis.