Find All Positive Values Of $u$ For Which the Series $\sum _ { m - 1 } ^ { \infty } 6 u ^ { \mathrm { m } 7 m }$

question 42

Multiple Choice

Find all positive values of $u$ for which the series $\sum _ { m - 1 } ^ { \infty } 6 u ^ { \mathrm { m } 7 m }$ converges. Select the correct answer.

• A) \(u > 7\)
• B) \(6 < u < \frac { 7 } { e }\)
• C) \(0 < u < \frac { 1 } { e }\)
• D) \(u < 6\)
• E) \(u > \ln 7\)

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Definitions:

Chloride

A negatively charged ion commonly found in salt compounds, essential for maintaining fluid balance and blood pressure.

Hypertonic Solution

A solution that has a higher concentration of solutes than the cytoplasm of cells, leading to osmotic pressure that may cause cell shrinkage.

Fluid Shift

The movement of bodily fluids from one compartment to another, affecting hydration status, blood volume, and pressure.

Osmosis

Movement of a pure solvent through a semipermeable membrane from a solution with a lower solute concentration to one with a higher solute concentration.