Determine the Sum of the Following Infinite Series $\sum _ { k = 0 } ^ { \infty } \left( \frac { 1 } { 3 } \right) ^ { k }$

question 17

Short Answer

Determine the sum of the following infinite series: $\sum _ { k = 0 } ^ { \infty } \left( \frac { 1 } { 3 } \right) ^ { k }$ $( 2 ) ^ { \mathrm { k } + 1 }$ .
Enter just an integer.

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Definitions:

Gas Chromatograph

An analytical instrument that measures the content of various components in a sample by separating and analyzing vapors.

Blank Sample

A sample without the analyte of interest, used as a control in analytical measurements.

Organic Compounds

Chemical compounds containing carbon atoms bonded to other carbon atoms or hydrogen atoms in a vast variety of structures, properties, and functions.

Petroleum-Based Chemicals

Chemical substances derived from crude oil and used in a variety of products and industrial processes.