Template:Sum

The following documentation is located at Template:Sum/doc. [<Edit> Template:Sum/doc]
[⧼Purge⧽ Template:Sum]

This template have been optimized (in the case of HTML+CSS typesetting) for Firefox,
though with some compromises to obtain [more or less] acceptable results with MS Internet Explorer (or now MS Edge) and Google Chrome.

The {{sum}} (summation operator) mathematical formatting template is used to obtain an HTML+CSS or a LaTeX formatted summation expression.

Usage

{{sum|from|to}} (followed by summand, as with LaTeX; format defaults to htm)

or

{{sum|from|to|format}} (followed by summand, as with LaTeX)

or

{{sum|from|to|summand}}

or

{{sum|from|to|summand|format}}

where format is one of the following:

• htm: HTML+CSS markup (text style, with postscript limits) for summation expression (default);
• HTM: HTML+CSS markup (display style, with underscript/overscript limits) for summation expression;
• tex: LaTeX markup (text style, with postscript limits) for summation expression;
• TEX: LaTeX markup (display style, with underscript/overscript limits) for summation expression.

Examples

The code

: line of text above{{nl}}another line of text above{{nl}}before {{math|{{sum|''i''{{=}}1|''n''|''i''{{^|3}}}}|&}} after{{nl}}line of text below{{nl}}another line of text below

yields the text style HTML+CSS

line of text above
another line of text above
before 

∑ n i  = 1  i 3

after
line of text below
another line of text below

The code

: line of text above{{nl}}another line of text above{{nl}}before {{math|{{sum|''i''{{=}}1|''n''|''i''{{^|3|tex}}|tex}}|$}} after{{nl}}line of text below{{nl}}another line of text below

yields the text style LaTeX

line of text above
another line of text above
before$\textstyle {\sum _{i=1}^{n}i^{3}}$ after
line of text below
another line of text below

The code

: {{math|{{sum|''i''{{=}}1|''n''|''i''{{^|3|HTM}}|HTM}}|&&}}

yields the display style HTML+CSS

n ∑   i  = 1   i 3

The code

: {{math|{{sum|''i''{{=}}1|''n''|''i''{{^|3|TEX}}|TEX}}|$$}}

yields the display style LaTeX

${\begin{array}{l}\displaystyle {\sum _{i=1}^{n}i^{3}}\end{array}}$

The code

: (...) "numbers {{math|''n''|tex = n|&}} such that <!--
-->{{math|''n''{{sp|2}}(''n'' + 1) {{=}} {{sum|''i''{{=}}1|''x''|(''n'' + ''i''{{sp|1}})}} {{=}} ''n''{{sp|1}}''x'' + {{sum|''i''{{=}}1|''x''|''i''}}
|tex = n (n + 1) = \sum_{i=1}^{x} (n + i) = nx + \sum_{i=1}^{x} i 
|&}} for some {{math|''x''|tex = x|&}}," except of course for the first term.

yields the text style HTML+CSS

(...) "numbers

n

such that

n  (n + 1) = ∑ x i  = 1  (n + i ) = n x + ∑ x i  = 1  i

for some

x

," except of course for the first term.

and, with the $ argument, yields the text style LaTeX

(...) "numbers $\textstyle {n}$ such that $\textstyle {n(n+1)=\sum _{i=1}^{x}(n+i)=nx+\sum _{i=1}^{x}i}$ for some $\textstyle {x}$," except of course for the first term.

Examples with fraction

The code

: before {{math|{{sum|''k''{{=}}1|infty|{{frac|''n''{{^|''k''}}|''n''!|htm}}|htm}}|&}} after

yields the text style HTML+CSS

before 

∑ ∞ k  = 1   n k n!

after

The code

: before {{math|{{sum|''k''{{=}}1|infty|{{frac|''n''{{^|''k''|tex}}|''n''!|tex}}|tex}}|$}} after

yields the text style LaTeX

before$\textstyle {\sum _{k=1}^{\infty }{\frac {n^{k}}{n!}}}$ after

The code

:{{math| {{sum|''k''{{=}}1|infty|{{frac|''n''{{^|''k''|HTM}}|''n''!|HTM}}|HTM}}|&&}}

yields the display style HTML+CSS

∞ ∑   k  = 1    n k n!

The code

: {{math|{{sum|''k''{{=}}1|infty|{{frac|''n''{{^|''k''|TEX}}|''n''!|TEX}}|TEX}}|$$}}

yields the display style LaTeX

${\begin{array}{l}\displaystyle {\sum _{k=1}^{\infty }{\frac {n^{k}}{n!}}}\end{array}}$

Examples with equality

The code

{{indent}}before {{math|{{fn|sin}} ''x'' {{=}} <!--
-->{{sum|''n''{{=}}1{{nl}}''n'' odd|{{sp|1}}{{nl}}infty|({{op|-}}1){{^|{{floor|''n''{{op|/}}2}}}}{{sp|6}}{{frac|''x''{{^|''n''}}|''n''!|htm}}}}
|&}} after

yields the text style HTML+CSS

     before 

sin  x = ∑   ∞ n  = 1 n odd  ( − 1)  ⌊  n / 2⌋   x n n!

after

The code

{{indent}}before {{math|{{fn|sin|tex}} ''x'' {{=}} <!--
-->{{sum|\stackrel{\scriptstyle ''n''{{=}}1}{''n'' \text{ odd} }|infty|({{op|-}}1){{^|{{floor|''n''/2|tex}}|tex}}{{sp|3|tex}}{{frac|''x''{{^|''n''|tex}}|''n''!|tex}}|tex}} 
|$}} after

yields the text style LaTeX

     before$\textstyle {{\sin }\,x=\sum _{\stackrel {\scriptstyle n=1}{n{\text{ odd}}}}^{\infty }({\,}-{\,}1)^{\lfloor {n/2}\rfloor }{\,}{\frac {x^{n}}{n!}}}$ after

The code

{{indent}}{{math|{{fn|sin}} ''x'' {{=}} <!--
-->{{sum|''n''{{=}}1{{nl}}''n'' odd|{{nl|2}}infty|({{op|-}}1){{^|{{floor|''n''{{op|/}}2}}|HTM}}{{sp|6}}{{frac|''x''{{^|''n''|HTM}}|''n''!|HTM}}|HTM}} 
|&&}}

yields the display style HTML+CSS

     

sin x =   ∞ ∑   n  = 1 n odd   (−1)  ⌊  n / 2⌋   x n n!

while the code

{{indent}}{{math|{{fn|sin|tex}} ''x'' {{=}} <!--
-->{{sum|\stackrel{\scriptstyle ''n''{{=}}1}{''n'' \text{ odd} }|infty|({{op|-}}1){{^|{{floor|''n''/2|tex}}|tex}} {{frac|''x''{{^|''n''|tex}}|''n''!|TEX}}|TEX}} 
|$$}}

yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {{\sin }\,x=\sum _{\stackrel {\scriptstyle n=1}{n{\text{ odd}}}}^{\infty }(-1)^{\lfloor {n/2}\rfloor }{\frac {x^{n}}{n!}}}\end{array}}$

Examples with nested summations

The code

: before {{math|<!--

-->{{sum|''i''{{=}}1|''p''<!--
-->|{{sum|''j''{{=}}1|''q''<!--
 -->|{{sum|''k''{{=}}1|''r''<!--
  -->|''a''{{sub|''i''{{sp|2}}''j''}}{{sp|2}}''b''{{sub|''j''{{sp|1}}''k''}}{{sp|3}}''c''{{sub|''k''{{sp|1}}''i''}}<!--
  -->|htm}}<!--
 -->|htm}}<!--
-->|htm}}<!--
--> 
|&}} after

yields the text style HTML+CSS

before 

∑ p i  = 1   ∑ q j  = 1   ∑ r k  = 1  ai  j  bj k ck i

after

while the code

: {{math|<!--

-->{{sum|''i''{{=}}1|''p''<!--
-->|{{sum|''j''{{=}}1|''q''<!--
 -->|{{sum|''k''{{=}}1|''r''<!--
  -->|''a''{{sub|''ij''|tex}}{{sp|2|tex}}''b''{{sub|''jk''|tex}}{{sp|3|tex}}''c''{{sub|''ki''|tex}}<!--
  -->|tex}}<!--
 -->|tex}}<!--
-->|tex}}<!--
--> 
|$}} after

yields the text style LaTeX

before$\textstyle {\sum _{i=1}^{p}\sum _{j=1}^{q}\sum _{k=1}^{r}a_{ij}{\!\,\!}{\;\!}b_{jk}{\!\,\!}{\,}c_{ki}{\!\,\!}}$ after

The code

: before {{math|<!--

-->{{sum|''i''{{=}}1|''p''<!--
-->|{{sum|''j''{{=}}1|''q''<!--
 -->|{{sum|''k''{{=}}1|''r''<!--
  -->|''a''{{sub|''i''{{sp|2}}''j''|HTM}}{{sp|2}}''b''{{sub|''j''{{sp|1}}''k''|HTM}}{{sp|2}}''c''{{sub|''k''{{sp|1}}''i''|HTM}}<!--
  -->|HTM}}<!--
 -->|HTM}}<!--
-->|HTM}}<!--
-->
|&&}}

yields the display style HTML+CSS

p ∑   i  = 1      q ∑   j  = 1      r ∑   k  = 1   ai  j  bj k  ck i

while the code

: {{math|<!--

-->{{sum|''i''{{=}}1|''p''<!--
-->|{{sum|''j''{{=}}1|''q''<!--
 -->|{{sum|''k''{{=}}1|''r''<!--
  -->|''a''{{sub|''ij''|tex}}{{sp|1|tex}}''b''{{sub|''jk''|tex}}{{sp|2|tex}}''c''{{sub|''ki''|tex}}<!--
  -->|TEX}}<!--
 -->|TEX}}<!--
-->|TEX}}<!--
-->
|$$}}

yields the display style LaTeX

${\begin{array}{l}\displaystyle {\sum _{i=1}^{p}\sum _{j=1}^{q}\sum _{k=1}^{r}a_{ij}{\!\,\!}{\;\;\!\!\!}b_{jk}{\!\,\!}{\;\!}c_{ki}{\!\,\!}}\end{array}}$

See also

• {{sum}} (summation)
• {{prod}} (product)
• {{int}} (simple integral: {{integral}} with int as type argument)
• {{integral}} (type argument: int, iint, iiint, iiiint, idotsint, oint, varointclockwise, ointctrclockwise, oiint, oiiint)