Determine If the Series Converges or Diverges; If the Series $$\sum _ { n = 0 } ^ { \infty } \frac { n ! } { 900 ^ { n } }$$

question 82

Multiple Choice

Determine if the series converges or diverges; if the series converges, find its sum.
- $$\sum _ { n = 0 } ^ { \infty } \frac { n ! } { 900 ^ { n } }$$

• A) Converges; \(\mathrm { e }\)
• B) Converges; 1
• C) converges; \(\frac { 1 } { \mathrm { e } }\)
• D) Diverges

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Definitions:

Poisson Distribution

A probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events happen with a known constant mean rate and independently of the time since the last event.

Occurrences

Instances or examples of something happening; events that take place.

Specified Interval

A defined range or period, often set for a particular purpose or task, indicating the precise limits within which something operates or occurs.

Binomial Experiment

An experiment having the four properties stated at the beginning of Section 5.5.