Find a Formula for the Nth Partial Sum of the Series

question 65

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.
- $$\frac { 8 } { 1 \cdot 3 } + \frac { 8 } { 2 \cdot 4 } + \frac { 8 } { 3 \cdot 5 } + \ldots + \frac { 8 } { n ( n + 2 ) } + \ldots$$

• A) \(\frac { 8 n ( 3 n + 4 ) } { 4 n ( n + 1 ) } ; 6\)
• B) \(\frac { 8 n ( 3 n + 5 ) } { 4 ( n + 1 ) ( n + 2 ) } ; 6\)
• C) \(\frac { 8 n ( 3 n + 5 ) } { 4 n ( n + 2 ) } ; 6\)
• D) \(\frac { 8 n ( 3 n + 4 ) } { 4 n ( n + 2 ) } ; 6\)

---

Definitions:

Less Elastic

Describes demand that is relatively insensitive to price changes, indicating consumers do not reduce purchase quantities significantly when prices increase.

Price Sensitive

Referring to the degree to which the demand for a product changes with a change in its price.

Cost Of Overpricing

The negative impacts, such as reduced sales and loss of market share, that can occur when a product is priced too high.

Cost Of Underpricing

The financial loss incurred by selling a product or service below its market value or cost, often to attract customers or gain market share.