Find the Partial Sum $S _ { 7 }$ Of the Series

question 28

Short Answer

Find the partial sum $S _ { 7 }$ of the series $\sum _ { m - 1 } ^ { \infty } \frac { 4 } { 10 + 7 ^ { m } }$ . Give your answer to five decimal places.

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Definitions:

Character Strengths

Positive traits reflected in thoughts, feelings, and behaviors that are considered virtues and contribute to an individual's fulfillment.

Positive Psychology

Positive Psychology is a branch of psychology focused on the study of what makes life most worth living, emphasizing positive human development, strengths, and flourishing.

Self-control

The ability to regulate one's emotions, thoughts, and behavior in the face of temptations and impulses.

Compassion

A deep awareness of and sympathy for another's suffering, coupled with the desire to alleviate that suffering.