Let $\sum a _ { n }$ And $\sum b _ { n }$

question 227

Essay

Let $\sum a _ { n }$ and $\sum b _ { n }$ be two series. Determine whether each of the following statements is true or false. Justify your answer.
(a) If $\sum a _ { n }$ converges, then $a _ { n } \rightarrow 0$ .
(b) If $a _ { n } \rightarrow 0$ , then $\sum a _ { n }$ converges.
(c) If $\sum a _ { n }$ converges, and $\sum b _ { n }$ diverges, then $\sum \left( a _ { n } + b _ { n } \right)$ diverges.
(d) If $\sum a _ { n }$ diverges, and $\sum b _ { n }$ diverges, then $\sum \left( a _ { n } + b _ { n } \right)$ diverges.
(e) If $\sum a _ { n }$ converges, and $\lim _ { n \rightarrow \infty } b _ { n } = 0$ then $\sum \left( a _ { n } + b _ { n } \right)$ converges.

Understand the historical and contemporary examples of how racial and ethnic identities can shift and evolve over time.

Evaluate the evidence and arguments against the biological determinism of social behaviors and traits.

Analyze how racial and ethnic labels and identities develop through negotiations, contestations, and social interactions.

Recognize the importance of promoting diverse role models to combat stereotypes and broaden representation.

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