Let $a _ { n } = \frac { 1 + 3 ^ { n } } { 1 + 4 \cdot 3 ^ { n } }$

question 209

Essay

Let $a _ { n } = \frac { 1 + 3 ^ { n } } { 1 + 4 \cdot 3 ^ { n } }$ .
(a) Find $\lim _ { n \rightarrow \infty } a _ { n }$ .
(b) Is $\sum a _ { n }$ convergent? Justify your answer.

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Definitions:

Outside Opinion

Perspectives or advice coming from individuals not directly involved in a situation or issue.

Pressure To Conform

The social influence that encourages individuals to match their attitudes, beliefs, or behaviors to group norms.

Groupthink

A phenomenon in social gatherings where the quest for accord or conformity fosters the development of decisions that are unsound or maladaptive.

Critical Ideas

Fundamental concepts or opinions that are considered important for understanding or analyzing a particular field or phenomena.