Determine Convergence or Divergence of the Alternating Series $$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \frac { 3 ( n + 1 ) ^ { 3 / 2 } } { n ^ { 3 / 2 } + 1 }$$

question 355

Multiple Choice

Determine convergence or divergence of the alternating series.
- $$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \frac { 3 ( n + 1 ) ^ { 3 / 2 } } { n ^ { 3 / 2 } + 1 }$$

• A) Converges
• B) Diverges

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Definitions:

Marginal Cost Curve

A graphical representation showing the change in total cost that arises from producing one additional unit of a good or service.

U-Shaped

A descriptive term for a scenario where performance or conditions decline, then bottom out, and finally improve, thus resembling the letter "U".

Average Variable Cost Curve

A graph that represents the variable costs of production divided by the quantity of output, illustrating how cost changes with changes in output.

U-Shaped

Describing a type of graph or relationship where the values fall, then rise, forming a shape similar to the letter "U".