Use the Root Test to Determine the Convergence or Divergence $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 4 n } { 3 n + 1 } \right) ^ { n }$$

question 38

Multiple Choice

Use the Root Test to determine the convergence or divergence of the series. $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 4 n } { 3 n + 1 } \right) ^ { n }$$

• A) converges
• B) diverges
• C) Root Test inconclusive

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Definitions:

Maladaptive Emotions

Emotional responses that are counter-productive and interfere with a person's ability to solve problems, relate to others, or achieve personal goals.

Rumination

The process of continuously thinking about the same thoughts, which are often sad or dark, for a prolonged period.

Stressful Experiences

Events or situations that cause significant strain, anxiety, or discomfort, often requiring adaptation or coping strategies.

Relaxation Response

A physiological state of deep rest that can be triggered by practices such as meditation, reducing stress and its adverse effects.