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:

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The unintentional flow of fluid between internal components of a system, such as in hydraulic or pneumatic systems, leading to reduced efficiency or failure.

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A specification of the general or approximate diameter of cylindrical components, such as pipes or fasteners, often used in engineering.

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A flexible tube used to convey hydraulic fluid between components in a hydraulic system, allowing for the transmission of power.