Find a Formula for the Nth Partial Sum of the Series

question 308

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

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

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Definitions:

Ethical Pluralism

The belief that there are multiple ethical principles or values that can be equally correct and fundamental in assessing moral questions, rejecting the idea of one universal moral truth.

Indifference

A lack of concern, interest, or sympathy towards others or a particular issue.

Openness

A personality trait or quality characterized by transparency, willingness to experience new things, and candid communication.

Use Of Force

The application of physical power or legal authority to control, restrain, or protect someone or something.