General Mathematics: Series, Sigma Notation, and Measurements Flashcards

Vocabulary flashcards covering mathematical series, sigma notation, and systems of measurement based on General Mathematics lecture notes.

Arithmetic Series

A result obtained by adding the terms of an arithmetic sequence, where each term increases or decreases by a constant difference.

Geometric Series

A series obtained by adding the terms of a geometric sequence, where each term is multiplied by a constant ratio and grows or shrinks exponentially.

Finite Geometric Series

The sum of a specific number of terms from a geometric sequence that has a beginning term and an ending term.

Infinite Geometric Series

The sum of a geometric sequence that goes on forever, which only has a sum if the terms get smaller and the common ratio $r$ satisfies $|r| < 1$.

Finite Series

A series that has a fixed number of terms.

Infinite Series

A series that does not have a pre-determined number of terms.

Sigma Notation

An explicit formula used to generalize and write a series in compact form using the Greek capital letter sigma ($\Sigma$), which means sum.

Index of Summation

The variable in sigma notation, represented by $k$ in the expression $\sum_{k=j}^{n} a_k$.

Lower Limit

The starting value of the index of summation in sigma notation, represented by $j$ in $\sum_{k=j}^{n} a_k$.

Upper Limit

The ending value of the index of summation in sigma notation, represented by $n$ in $\sum_{k=j}^{n} a_k$.

English System

Also called the Imperial System, a measurement system founded in Medieval England with units based on everyday references such as the inch, foot, and yard.

Metric System

A system of measurement that uses standard units such as meters for length, liters for volume, and grams for mass.

International System of Units (SI)

A globally standardized system developed from the metric system in 1960 that features seven base units for measuring physical quantities.

Unit Conversion

The process of changing a measurement from one unit to another subunit.

Scale

A representation showing how the distance on a map or drawing compares to the actual distance in real life.

Large Scale

A map scale with a smaller consequent that covers a small area with more precise details.

Small Scale

A map scale with a large consequent that covers a large area with little detail.