Given the Series $\sum _ { m = 1 } ^ { \infty } \frac { 3 m } { 4 ^ { m } ( 3 m + 5 ) }$

question 49

Short Answer

Given the series $\sum _ { m = 1 } ^ { \infty } \frac { 3 m } { 4 ^ { m } ( 3 m + 5 ) }$ estimate the error in using the partial sum $s _ { 8 }$ by comparison with the series $\sum _ { m = 9 } ^ { \infty } \frac { 1 } { 4 ^ { m } }$ .

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Definitions:

Pill Cap Microprocessor

A technology used in medication caps that tracks when a medication is taken and can remind patients about their medication schedules through digital means.

Adherence Assessment

The evaluation of how well a patient follows a prescribed treatment regimen, including medication, lifestyle changes, and other therapy forms.

Chronic Conditions

Long-lasting health conditions that can be managed but not always cured.

Adherence Rates

The extent to which patients take medications or follow medical instructions as prescribed by healthcare providers.