This site is supported by donations to The OEIS Foundation.

# Template:Nroot/doc/Mathematical examples

The code (“partial multipliers” 1 are automatically blanked)

: {{math|[[Golden ratio|''{{Gr|phi}}'']] {{=|sp}} {{nroot|;; 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//|HTM}}
|tex = \phi = {{nroot|;; 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//|TEX}}
|&&}}


yields the display style HTML+CSS

 ϕ  =    2√  1 +   2√  1 +   2√  1 +   2√  1 +   2√  1 +   2√  1 +   2√  1 +   2√  ⋯

The code (“partial multipliers” 1 are automatically blanked)

: {{math|[[Golden ratio|''{{Gr|phi}}'']] {{=|sp}} {{nroot|;; 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//|HTM}}
|tex = \phi = {{nroot|;; 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//1,, 1//|TEX}}
|$$}}  yields the display style LaTeX ${\displaystyle {\begin{array}{l}\displaystyle {\phi ={\sqrt {1\,+\,{\sqrt {1\,+\,{\sqrt {1\,+\,{\sqrt {1\,+\,{\sqrt {1\,+\,{\sqrt {1\,+\,{\sqrt {1\,+\,{\sqrt {\cdots }}}}}}}}}}}}}}}}}\end{array}}}$ The code (“partial radicands” 0 are automatically blanked) : {{math|''x''{{^|''e''{{op|-}}{{sp|-1}}1}} {{=|sp}} {{nroot|;; ''x''//0//,, ''x''//0//3,, ''x''//0//4,, ''x''//0//5,, ''x''//0//6,, ''x''//0//7,, ''x''//0//8,, ''x''// //9|HTM}} |tex = x^{e-1} = {{nroot|;; ''x''//0//,, ''x''//0//3,, ''x''//0//4,, ''x''//0//5,, ''x''//0//6,, ''x''//0//7,, ''x''//0//8,, ''x''// //9|TEX}} |&&}}  yields the display style HTML+CSS  x e − 1 = x 2√ x 3√ x 4√ x 5√ x 6√ x 7√ x 8√ x 9√ ⋯ The code (“partial radicands” 0 are automatically blanked) : {{math|''x''{{^|''e''{{op|-}}{{sp|-1}}1}} {{=|sp}} {{nroot|;; ''x''//0//,, ''x''//0//3,, ''x''//0//4,, ''x''//0//5,, ''x''//0//6,, ''x''//0//7,, ''x''//0//8,, ''x''// //9|HTM}} |tex = x^{e-1} = {{nroot|;; ''x''//0//,, ''x''//0//3,, ''x''//0//4,, ''x''//0//5,, ''x''//0//6,, ''x''//0//7,, ''x''//0//8,, ''x''// //9|TEX}} |$$}}


yields the display style LaTeX

${\displaystyle {\begin{array}{l}\displaystyle {x^{e-1}={x{\sqrt {x{\sqrt[{3}]{x{\sqrt[{4}]{x{\sqrt[{5}]{x{\sqrt[{6}]{x{\sqrt[{7}]{x{\sqrt[{8}]{x{\sqrt[{9}]{\cdots }}}}}}}}}}}}}}}}}}\end{array}}}$

The code

: {{math|{{frac|2|{{Gr|pi}}|HTM}} {{=|sp}} <!--
-->{{nroot|;; 1//{{tfrac|1|2}}|HTM}} {{nroot|;; 1//{{tfrac|1|2}},, {{tfrac|1|2}}//{{tfrac|1|2}}|HTM}} {{nroot|;; 1//{{tfrac|1|2}},, {{tfrac|1|2}}//{{tfrac|1|2}},, {{tfrac|1|2}}//{{tfrac|1|2}}|HTM}} {{...|cdots}}
|tex = \frac{2}{\pi} = <!--
-->{{nroot|;; 1//\tfrac{1}{2}|TEX}} \ {{nroot|;; 1//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2}|TEX}} \ {{nroot|;; 1//\tfrac{1}{2},, <!--
-->\tfrac{1}{2}//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2}|TEX}} \ \cdots
|&&}}


yields the display style HTML+CSS

 Error: String exceeds 10,000 character limit.

The code

: {{math|{{frac|2|{{Gr|pi}}|HTM}} {{=|sp}} <!--
-->{{nroot|;; 1//{{tfrac|{{sp|1}}1{{sp|1}}|2}}|HTM}} {{nroot|;; 1//{{tfrac|{{sp|1}}1{{sp|1}}|2}},, {{tfrac|{{sp|1}}1{{sp|1}}|2}}{{sp|1}}//{{tfrac|{{sp|1}}1{{sp|1}}|2}}|HTM}}{{sp|3}}
|tex = \frac{2}{\pi} = {{nroot|;; 1//\tfrac{1}{2}|TEX}} ~ {{nroot|;; 1//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2}|TEX}}|&&}}<!--

Broken in two parts to avoid the pesky 10,000 characters limit for template argument size.

-->{{math|{{nroot|;; 1//{{tfrac|{{sp|1}}1{{sp|1}}|2}},, {{tfrac|{{sp|1}}1{{sp|1}}|2}}{{sp|1}}//{{tfrac|{{sp|1}}1{{sp|1}}|2}},, {{tfrac|{{sp|1}}1{{sp|1}}|2}}{{sp|1}}//{{tfrac|{{sp|1}}1{{sp|1}}|2}}|HTM}} {{sp|3}}{{...|cdots}}
|tex = {{nroot|;; 1//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2}|TEX}} ~ \cdots|&&}}

 2 π
=    2
 1 2
2
 1 2
+
 1 2
2
 1 2
2
 1 2
+
 1 2
2
 1 2
+
 1 2
2
 1 2

The code

: {{math|{{frac|2|{{Gr|pi}}|HTM}} {{=|sp}} <!--
-->{{nroot|;; 1//{{tfrac|1|2}}|HTM}} {{nroot|;; 1//{{tfrac|1|2}},, {{tfrac|1|2}}//{{tfrac|1|2}}|HTM}} {{nroot|;; 1//{{tfrac|1|2}},, {{tfrac|1|2}}//{{tfrac|1|2}},, {{tfrac|1|2}}//{{tfrac|1|2}}|HTM}} {{...|cdots}}
|tex = \frac{2}{\pi} = <!--
-->{{nroot|;; 1//\tfrac{1}{2}|TEX}} \ {{nroot|;; 1//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2}|TEX}} \ {{nroot|;; 1//\tfrac{1}{2},, <!--
-->\tfrac{1}{2}//\tfrac{1}{2},, \tfrac{1}{2}//\tfrac{1}{2}|TEX}} \ \cdots
|}}


yields the display style LaTeX

${\displaystyle {\begin{array}{l}\displaystyle {{\frac {2}{\pi }}={\sqrt {\tfrac {1}{2}}}\ {\sqrt {{\tfrac {1}{2}}\,+\,{\tfrac {1}{2}}{\sqrt {\tfrac {1}{2}}}}}\ {\sqrt {{\tfrac {1}{2}}\,+\,{\tfrac {1}{2}}{\sqrt {{\tfrac {1}{2}}\,+\,{\tfrac {1}{2}}{\sqrt {\tfrac {1}{2}}}}}}}\ \cdots }\end{array}}}$