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< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < mi > S< / mi > < mo stretchy = "false" > (< / mo > < mi > n< / mi > < mo stretchy = "false" > )< / mo > < mo > =< / mo > < mrow > < mo fence = "true" > {< / mo > < mtable rowspacing = "0.3599999999999999em" columnalign = "left left" columnspacing = "1em" > < mtr > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mn > 0< / mn > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < mtext > if < / mtext > < mi > n< / mi > < mo > =< / mo > < mn > 0< / mn > < / mrow > < / mstyle > < / mtd > < / mtr > < mtr > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < mi > n< / mi > < mo > +< / mo > < mi > S< / mi > < mo stretchy = "false" > (< / mo > < mi > n< / mi > < mo > − < / mo > < mn > 1< / mn > < mo stretchy = "false" > )< / mo > < / mrow > < / mstyle > < / mtd > < mtd > < mstyle scriptlevel = "0" displaystyle = "false" > < mrow > < mtext > if < / mtext > < mi > n< / mi > < mo > > < / mo > < mn > 0< / mn > < / mrow > < / mstyle > < / mtd > < / mtr > < / mtable > < / mrow > < / mrow > < annotation encoding = "application/x-tex" >
S(n) = \begin{cases}
0 & \text{if } n=0\\
n+S(n-1) & \text{if } n> 0
\end{cases}
< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1em;vertical-align:-0.25em;" > < / span > < span class = "mord mathdefault" style = "margin-right:0.05764em;" > S< / span > < span class = "mopen" > (< / span > < span class = "mord mathdefault" > n< / span > < span class = "mclose" > )< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:3.0000299999999998em;vertical-align:-1.25003em;" > < / span > < span class = "minner" > < span class = "mopen delimcenter" style = "top:0em;" > < span class = "delimsizing size4" > {< / span > < / span > < span class = "mord" > < span class = "mtable" > < span class = "col-align-l" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.69em;" > < span style = "top:-3.69em;" > < span class = "pstrut" style = "height:3.008em;" > < / span > < span class = "mord" > < span class = "mord" > 0< / span > < / span > < / span > < span style = "top:-2.25em;" > < span class = "pstrut" style = "height:3.008em;" > < / span > < span class = "mord" > < span class = "mord mathdefault" > n< / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mord mathdefault" style = "margin-right:0.05764em;" > S< / span > < span class = "mopen" > (< / span > < span class = "mord mathdefault" > n< / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mbin" > − < / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mord" > 1< / span > < span class = "mclose" > )< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:1.19em;" > < span > < / span > < / span > < / span > < / span > < / span > < span class = "arraycolsep" style = "width:1em;" > < / span > < span class = "col-align-l" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:1.69em;" > < span style = "top:-3.69em;" > < span class = "pstrut" style = "height:3.008em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > if < / span > < / span > < span class = "mord mathdefault" > n< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < span style = "top:-2.25em;" > < span class = "pstrut" style = "height:3.008em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > if < / span > < / span > < span class = "mord mathdefault" > n< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mord" > 0< / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:1.19em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mclose nulldelimiter" > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
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