Rewrite $\sum _ { i = 1 } ^ { n } \frac { 9 i ^ { 3 } } { n ^ { 5 } }$

question 12

Multiple Choice

Rewrite $\sum _ { i = 1 } ^ { n } \frac { 9 i ^ { 3 } } { n ^ { 5 } }$ as a rational function $S ( n )$ and find $\lim _ { n \rightarrow \infty } S ( n )$ .

• A) \(S ( n ) = \frac { 9 ( n + 1 ) ^ { 2 } } { 4 n ^ { 2 } } , \lim _ { n \rightarrow \infty } S ( n ) = \frac { 9 } { 4 }\)
• B) \(S ( n ) = \frac { 9 n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } , \lim _ { n \rightarrow \infty } S ( n ) = 9\)
• C) \(S ( n ) = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 36 } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• D) \(S ( n ) = \frac { 9 ( n + 1 ) ^ { 2 } } { 4 n ^ { 3 } } , \lim _ { n \rightarrow \infty } S ( n ) = 0\)
• E) \(S ( n ) = \frac { 9 ( n + 1 ) ^ { 2 } } { 4 n ^ { 3 } }\), the limit does not exist

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Definitions:

Narrative Counselors

Therapists who use narrative therapy, focusing on the stories that individuals create about their lives and exploring ways to rewrite these narratives in more empowering ways.

Exception Questions

Questions asked within therapy to help clients identify times when the problem did not occur, suggesting alternative patterns or solutions.

Scaffolding

Scaffolding is an educational approach that involves providing support to students or individuals as they learn new concepts, gradually removing the support as they become more proficient.

Action Plans

Detailed strategies or steps designed to achieve specific goals or outcomes.