Find a Formula for the Nth Partial Sum of the Series

question 31

Multiple Choice

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.
- $$7 + \frac { 7 } { 4 } + \frac { 7 } { 16 } + \ldots + \frac { 7 } { 4 ^ { n - 1 } } + \ldots$$

• A) \(\frac { \left( 1 - \frac { 1 } { 4 ^ { n } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 5 }\)
• B) \(\frac { 7 \left( 1 - \frac { 1 } { 4 ^ { n - 1 } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 5 }\)
• C) \(\frac { 7 \left( 1 - \frac { 1 } { 4 ^ { n - 1 } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 3 }\)
• D) \(\frac { 7 \left( 1 - \frac { 1 } { 4 ^ { n } } \right) } { 1 - \frac { 1 } { 4 } } ; \frac { 28 } { 3 }\)

---

Definitions:

Non-Verbal Communication

The process of conveying a message without the use of words, which can include facial expressions, body language, and gestures.

Non-Verbal Communication

The process of transferring information through behaviors and cues rather than words, such as body language, gestures, and facial expressions.

Hedges

Linguistic terms or phrases used to soften statements, making them less direct or certain, often to express politeness or uncertainty.

Non-Verbal Behaviour

Non-verbal behavior includes all forms of communication that do not involve the spoken word, such as body language, gestures, facial expressions, and eye contact.