Determine If the Series Converges or Diverges; If the Series $$\sum _ { n = 0 } ^ { \infty } \frac { 1 } { ( \sqrt { 5 } ) ^ { n } }$$

question 129

Multiple Choice

Determine if the series converges or diverges; if the series converges, find its sum.
- $$\sum _ { n = 0 } ^ { \infty } \frac { 1 } { ( \sqrt { 5 } ) ^ { n } }$$

• A) Converges; \(\frac { \sqrt { 5 } - 5 } { 4 }\)
• B) Converges; \(\frac { 5 + \sqrt { 5 } } { 4 }\)
• C) Converges; \(\frac { 5 - \sqrt { 5 } } { 4 }\)
• D) Diverges

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Definitions:

Economies of Scale

Cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output decreasing as scale increases.

Diseconomies of Scale

The phenomenon where production costs increase as a firm expands output, leading to reduced efficiency.

U-Shaped Long-Run Average Cost Curve

This describes the phenomenon where, over time, average costs first decrease with increased production, hit a minimum, and then increase with further production increase, forming a U-shape.

Minimum Cost

The lowest possible expense at which a particular set of goods or services can be produced or acquired.