Find a Formula for the Nth Partial Sum of the Series

question 137

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.
- $$\frac { 7 } { 2 \cdot 3 } + \frac { 7 } { 3 \cdot 4 } + \frac { 7 } { 4 \cdot 5 } + \ldots + \frac { 7 } { ( n + 1 ) ( n + 2 ) } + \ldots$$

• A) \(\frac { 7 n } { n + 2 } ; 7\)
• B) \(\frac { 7 n } { 2 ( n + 1 ) } ; \frac { 7 } { 2 }\)
• C) \(\frac { 7 n } { 2 ( n + 2 ) } ; \frac { 7 } { 2 }\)
• D) \(\frac { 7 n } { n + 1 } ; 7\)

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Definitions:

Sensation

The process by which our sensory receptors and nervous system receive and represent stimulus energies from our environment.

Sensory Information

Data that is received through the senses, such as sight, hearing, smell, taste, and touch, which is then processed by the nervous system.

Subliminal Messages

Hidden or disguised messages that are not consciously perceived but may influence an individual's thoughts, behaviors, or actions.

Absolute Threshold

The minimum intensity of a stimulus at which it can be detected by an observer 50% of the time.