Write Sum Using Sigma Notation

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Sigma Notation of a Series

A series can be represented in a compact form, called summation or sigma notation. The Greek uppercase, $\sum$ , is used to represent the sum.

The series

$\mathrm{iv}+8+12+16+\mathrm{twenty}+24$

tin can be expressed as

${\displaystyle \sum _{n=1}^{\mathrm{half\; dozen}}\mathrm{four}n}$

. The expression is read as the sum of

$4n$

as

$n$

goes from

$1$

to

$\mathrm{vi}$

. The variable

$\mathrm{north}$

is called the index of summation.

To generate the terms of a series given in sigma notation, successively supplant the alphabetize of summation with consecutive integers from the first value to the terminal value of the index.

To generate the terms of the series given in sigma notation in a higher place, replace $\mathrm{north}$ past $1,\mathrm{ii},\mathrm{iii},\mathrm{four},5,\text{and}6$ .

$\begin{array}{l}{\displaystyle \sum _{n=1}^{\mathrm{half-dozen}}4n}=4\left(1\right)+\mathrm{four}\left(2\right)+\mathrm{iv}\left(3\right)+4\left(4\right)+4\left(5\right)+4\left(6\right)\\ =4+\mathrm{eight}+12+16+20+24\\ =84\end{array}$

The sum of the series is $84$ .

To acquire more about ${\mathrm{Southward}}_{\mathrm{northward}}$ notation, view this lesson: Sum of the First northward Terms of a Serial

Write Sum Using Sigma Notation,

Source: https://www.varsitytutors.com/hotmath/hotmath_help/topics/sigma-notation-of-a-series

Posted by: cartwrightpospot.blogspot.com

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