document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916883>Question 916883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having difficulty understanding double summations.  Is there a good explanation you can recommend?<BR>\n" );
document.write( "<br>Here's one of the problems:<BR>\n" );
document.write( "(first summation) upper limit=2, lower limit i=0<BR>\n" );
document.write( "(second summation) upper limit=3, lower limit j=0<BR>\n" );
document.write( "function: 2i+3j<BR>\n" );
document.write( "Do I just do them separately and then add?  Confused... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556361 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \sum_{i=0}^2\,\sum_{j=0}^3\,2i\ +\ 3j\">\r<BR>\n" );
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document.write( "First term of the sum: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 0\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 0\">\r<BR>\n" );
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document.write( "Second term of the sum:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 0\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 1\">\r<BR>\n" );
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document.write( "Third term of the sum: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 0\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 2\">\r<BR>\n" );
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document.write( "Fourth term: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 0\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 3\">\r<BR>\n" );
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document.write( "Fifth term: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 1\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 0\">\r<BR>\n" );
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document.write( "Sixth term: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 1\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 1\">\r<BR>\n" );
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document.write( "...\r<BR>\n" );
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document.write( "Next to the last term: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 2\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 2\">\r<BR>\n" );
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document.write( "Last term: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large i\ =\ 2\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\ =\ 3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  = (2*0+3*0)\ +\ (2*0+3*1)\ +\ (2*0+3*2)\ +\ (2*0+3*3)\ +\ (2*1+3*0)\ +\ ...\">\r<BR>\n" );
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document.write( "and so on...\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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