Use the Direct Comparison Test to Determine the Convergence or Divergence

question 20

Multiple Choice

Use the Direct Comparison Test to determine the convergence or divergence of the series $$\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 5 ^ { 4 } \sqrt { n } - 1 }$$

• A) The series \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 5 ^ { 4 } \sqrt { n } - 1 }\) converges.
• B) The series \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 5 ^ { 4 } \sqrt { n } - 1 }\) diverges.

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Definitions:

Exponential Smoothing

A forecasting technique that applies diminishing weights to past observations, with recent observations given more weight than older observations.

Weights

Factors that adjust the importance or influence of different items in a calculation, often used in statistical analysis and algorithms.

Linear Trend

A trend that consistently increases or decreases at a steady rate over a period of time.

Time Periods

Specific intervals or spans of time during which certain events or measurements are taken or analyzed.