Determine the Sum of the Infinite Geometric Series $\sum _ { \mathrm { k } = 0 } ^ { \infty } 3 ^ { - \mathrm { k } } \ln 2$

question 100

Short Answer

Determine the sum of the infinite geometric series $\sum _ { \mathrm { k } = 0 } ^ { \infty } 3 ^ { - \mathrm { k } } \ln 2$ Enter your answer exactly in the reduced form $\frac { a \ln b } { c }$ .

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Definitions:

Fatty Acids

Long chains of hydrocarbon molecules with a carboxylic acid group, which are components of lipids and play roles in energy storage and cellular structure.

Potassium Ion

A positively charged ion (K+) essential for various biological processes, including nerve transmission and muscle contraction.

Simple Diffusion

The movement of molecules from an area of higher concentration to an area of lower concentration without the need for energy input or assistance of membrane proteins.

Cellular Membrane

The cellular membrane, or plasma membrane, is the biological membrane that separates the interior of all cells from the outside environment, controlling the movement of substances in and out of cells.