# LibreOffice Math: Sigma Equation Examples

This article provides sigma equation examples for LibreOffice Math. Below, you get the codes so you can run them in Math and alo in Writer documents. You can download the sample documents below for Math and Writer to change and share them as you wish. This article is a part of LibreOffice Math the series (Getting Started, Matrix, Integrals, Limits) to help teachers in schools and universities teach using LibreOffice.

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## How It Looks

Here is how the code looks in LibreOffice Math and Writer.

## Example 1

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Code:

sum from{ i=1 } to{ n } i = { n(n+1) } over { 2 }

## Example 2

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Code:

sum from{ i=m } to{ n } a_i = a_m + a_{m+1} + a_{ m+2 } + ... + a_{ n-1 } + a_n
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sum from{ i=3 } to{ 6 } i^2 = 3^2 + 4^2 + 5^2 + 6^2 = 86.
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## Example 3

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sum a^2_i = sum from{ i=1 } to{ n } {a^2_1}.
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## Example 4

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Code:

sum from{ i=a } to{ b } g( i ) = 0, {}{} for {}{} b < a.
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sum from{ i=a } to{ b } g( i ) = g( b ) + sum from{ i=a } to{ b=1 } g( i ), { }{ } for {  }{  } b>= a.
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## Example 5

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sum from{ k=a } to{ b } f( k ) = f_{ [a,b] } f d%imu
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## Example 6

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sum from{ k=a } to{ b } f( k ) = %DELTA^-1 f( b+1 ) - %DELTA^-1 f( a )
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## Example 7

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int from{ s=a-1 } to{ b } f( s ) ds <= sum from{ i=a } to{ b } f( i ) <= int from{ s=a } to{ b+1 } f( s ) ds.
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int from{ s=a } to{ b+1 } f( s ) ds <= sum from{ i=a } to{ b } f( i ) <= int from{ s=a-1 } f( s ) ds.
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## Example 8

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Code:

{ b-a }over{ n } sum from{ i=0 } to{ n-1 } f( a+i{b-a}over{n} ) approx int from{ a } to{ b } f( x ) dx,
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## Example 9

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Code:

sum from{ i=m } to{ n-1 } a^i = ( a^m - a^n ) over ( 1-a ) ; ( m < n )
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sum from{ i=0 } to{ n-1 } i2^i = 2 + ( n-2 )2^n ( special case when a = 2 )
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## Example 10

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Code:

sum from{ i=m } to{ n } 1 = n + 1 - m
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sum from{ i=m } to{ n } i = { n(n+1) }over{ 2 } - { m(m-1) }over{ 2 } = { (n+1-m)(n+m) }over{ 2 }
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