Approximate the Sum to the Indicated Accuracy $\sum _ { n = 1 } ^ { \infty } \frac { 4 ( - 1 ) ^ { n - 1 } } { n ^ { 7 } }$

question 120

Short Answer

Approximate the sum to the indicated accuracy.
$\sum _ { n = 1 } ^ { \infty } \frac { 4 ( - 1 ) ^ { n - 1 } } { n ^ { 7 } }$ (five decimal places)

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Definitions:

Early Diagnosis

The process of identifying a disease or condition at a preliminary stage, allowing for more effective treatment.

Effective Treatment

Therapeutic interventions or methods that have been scientifically proven to improve health outcomes or ameliorate symptoms.

Calorie Consumption

The total number of calories ingested through food and drink over a period of time, which is critical for managing weight and energy balance.

Health-Impairing Behaviours

Actions or habits that negatively affect an individual's health, such as smoking, excessive drinking, and poor diet.