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<A NAME=SUM>

<TITLE>SUM</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>SUM</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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The operator <em>sum</em> returns 
the indefinite or definite summation of a given expression. 
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<P>
 <P> <H3> 
syntax: </H3>
<em>sum</em>(&lt;expr&gt;,&lt;k&gt;[,&lt;lolim&gt; [,&lt;uplim&gt; ]]) 
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where &lt;expr&gt; is the expression to be added, &lt;k&gt; is the 
control variable (a 
<A HREF=r37_0002.html>kernel</A>), and &lt;lolim&gt; and &lt;uplim&gt; 
are the optional lower and upper limits. If &lt;uplim&gt; is 
not supplied the upper limit is taken as &lt;k&gt;. The Gosper 
algorithm is used. If there is no closed form solution, the operator 
returns the input unchanged. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
sum(4n**3,n); 

   2    2
  n  *(n   + 2*n + 1)


sum(2a+2k*r,k,0,n-1);

  n*(2*a + n*r - r)

</TT></PRE><P>