Find a Formula for the Nth Partial Sum of the Series

question 59

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.
- $$\frac { 9 } { 1 \cdot 2 \cdot 3 } + \frac { 9 } { 2 \cdot 3 \cdot 4 } + \frac { 9 } { 3 \cdot 4 \cdot 5 } + \ldots + \frac { 9 } { n ( n + 1 ) ( n + 2 ) } + \ldots$$

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

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