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) \(\frac { 8 n ( 3 n + 4 ) } { 4 n ( n + 2 ) } ; 6\)

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Definitions:

Purchasing-Power Parity

A theory that states that in the absence of transaction costs and barriers to trade, the exchange rate between two currencies should equalize the purchasing power of the two currencies.

Nominal Exchange Rate

The rate at which one currency can be exchanged for another currency, without adjusting for inflation differences between the two countries.

Real Exchange Rate

A measure that compares the relative price of a basket of goods between two countries, adjusted for currency exchange rates.

Basket Of Goods

A set of products and services, considered a representative sample, used to measure the change in overall price levels over time, such as in the calculation of inflation.