A Series $\sum _ { k = 1 } ^ { \infty } a _ { k }$

question 8

Essay

A series $\sum _ { k = 1 } ^ { \infty } a _ { k }$ has partial sums, $S _ { n }$ , given by $S _ { n } = \frac { 7 n - 2 } { n }$ (a) Is $\sum _ { k = 1 } ^ { \infty } a _ { k }$ convergent? If it is, find the sum.(b) Find $\lim _ { n \rightarrow \infty } a _ { k }$ .(c) Find $\sum _ { k = 1 } ^ { 200 } a _ { k }$

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Definitions:

Investigative Dimension

A characteristic or aspect pertaining to the systematic examination or exploration of subjects, often related to one's interests in solving problems or understanding phenomena.

Holland Scales

A theory and assessment tool that categorizes vocational interests into six types to help individuals identify suitable career paths.

Big Five Dimension

A model that outlines five major dimensions of human personality: openness, conscientiousness, extraversion, agreeableness, and neuroticism.

Holland's RIASEC

A theory of careers and vocational choice based upon personality types, with the six types being Realistic, Investigative, Artistic, Social, Enterprising, and Conventional.