Find a Formula for the Nth Partial Sum of the Series

question 87

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.
- $$\frac { 6 } { 1 \cdot 3 } + \frac { 6 } { 2 \cdot 4 } + \frac { 6 } { 3 \cdot 5 } + \ldots + \frac { 6 } { n ( n + 2 ) } + \ldots$$

• A) \(\frac { 6 n ( 3 n + 4 ) } { 4 n ( n + 2 ) } ; \frac { 9 } { 2 }\)
• B) \(\frac { 6 n ( 3 n + 4 ) } { 4 n ( n + 1 ) } ; \frac { 9 } { 2 }\)
• C) \(\frac { 6 n ( 3 n + 5 ) } { 4 n ( n + 2 ) } ; \frac { 9 } { 2 }\)
• D) \(\frac { 6 n ( 3 n + 5 ) } { 4 ( n + 1 ) ( n + 2 ) } ; \frac { 9 } { 2 }\)

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Definitions:

Standard Deviation

A mathematical indicator assessing the extent of spread within a collection of data points.

Sampling Distribution

The probability distribution of a statistic obtained from a large number of samples drawn from a specific population.

Normal Population

A population in statistics where all the individual measurements are symmetrically distributed around the mean, following a normal distribution.

Standard Deviation

A statistical metric that evaluates the spread of data points in a dataset around the mean.