Use the Direct Comparison Test to Determine the Convergence or Divergence

question 121

Multiple Choice

Use the Direct Comparison Test to determine the convergence or divergence of the series $\sum _ { n = 1 } ^ { \infty } \frac { 7 n } { \left( n ^ { 2 } + 7 \right) ^ { 2 } }$ .

• A)
• The series \(\sum _ { n = 1 } ^ { \infty } \frac { 7 n } { \left( n ^ { 2 } + 7 \right) ^ { 2 } }\) diverges.
• B)
• The series \(\sum _ { n = 1 } ^ { \infty } \frac { 7 n } { \left( n ^ { 2 } + 7 \right) ^ { 2 } }\) converges.

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Definitions:

Transformational Leadership Factors

Elements that contribute to transformational leadership, including inspirational motivation, individualized consideration, intellectual stimulation, and idealized influence.

Transformational Leadership

A leadership approach that causes change in individuals and social systems, characterized by the leader working with teams to identify needed change, creating a vision to guide the change through inspiration, and executing the change in tandem with committed members of the group.

Intellectual Stimulation

A leadership behavior that encourages followers to think critically and creatively, challenging existing assumptions and suggesting new perspectives.

Inspirational Motivation

The ability to inspire and motivate others towards achieving shared goals through enthusiasm and positive reinforcement.