Find a Formula for the Nth Partial Sum of the Series

question 257

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.
- $$\frac { 18 } { 1 ^ { 2 } \cdot 2 ^ { 2 } } + \frac { 30 } { 2 ^ { 2 } \cdot 3 ^ { 2 } } + \frac { 42 } { 3 ^ { 2 } \cdot 4 ^ { 2 } } + \ldots + \frac { 6 ( 2 n + 1 ) } { n ^ { 2 } ( n + 1 ) ^ { 2 } } + \ldots$$

• A) \(\frac { 6 n ^ { 2 } } { ( n + 1 ) ( n + 2 ) } ; 6\)
• B) \(\frac { 6 n ( n + 1 ) } { ( n + 2 ) ^ { 2 } } ; 6\)
• C) \(\frac { 6 ( \mathrm { n } + 1 ) ( \mathrm { n } + 2 ) } { \mathrm { n } ^ { 2 } } ; 6\)
• D) \(\frac { 6 n ( n + 2 ) } { ( n + 1 ) ^ { 2 } } ; 6\)

Acquire knowledge about the glycemic index and its application in diet planning for weight management and diabetes control.

Learn the importance of dietary fibers and their sources, differentiating between soluble and insoluble types.

Understand the concept of correlation and discern between positive, negative, and null correlations.

Comprehend the significance of statistical significance in research findings.

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