document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104112>Question 1104112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of the series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F%28sqrt+%282%29+%2B+sqrt+%281%29%29+%2B+5%2F%28sqrt+%283%29+%2B+sqrt+%282%29%29+%2B+5%2F%28sqrt+%284%29+%2B+sqrt+%283%29%29+%2B5%2F%28sqrt+%285%29+%2B+sqrt+%284%29%29+%2B...+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F%28sqrt+%2836%29+%2B+sqrt+%2835%29%29+ ALIGN=MIDDLE  ALT=\"+5%2F%28sqrt+%2836%29+%2B+sqrt+%2835%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718879 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let's look at the sum of the first few terms of the series; then you can use that to predict the sum of the whole series.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F%28sqrt+%282%29+%2B+sqrt+%281%29%29+=%285%2F%28sqrt+%282%29+%2B+sqrt+%281%29%29%29%2A%28%28sqrt%282%29-sqrt%281%29%29%2F%28sqrt%282%29-sqrt%281%29%29%29+=+5%2A%28%28sqrt%282%29-sqrt%281%29%29%2F%282-1%29%29+=+5%2A%28sqrt%282%29-sqrt%281%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F%28sqrt+%283%29+%2B+sqrt+%282%29%29+=%285%2F%28sqrt+%283%29+%2B+sqrt+%282%29%29%29%2A%28%28sqrt%283%29-sqrt%282%29%29%2F%28sqrt%283%29-sqrt%282%29%29%29+=+5%2A%28%28sqrt%283%29-sqrt%282%29%29%2F%283-2%29%29+=+5%2A%28sqrt%283%29-sqrt%282%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F%28sqrt+%284%29+%2B+sqrt+%283%29%29+=%285%2F%28sqrt+%284%29+%2B+sqrt+%283%29%29%29%2A%28%28sqrt%284%29-sqrt%283%29%29%2F%28sqrt%284%29-sqrt%283%29%29%29+=+5%2A%28%28sqrt%284%29-sqrt%283%29%29%2F%284-3%29%29+=+5%2A%28sqrt%284%29-sqrt%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the sum of the first three terms of the series is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28sqrt%282%29-sqrt%281%29%29%2B5%2A%28sqrt%283%29-sqrt%282%29%29%2B5%2A%28sqrt%284%29-sqrt%283%29%29+=+5%2A%28%28sqrt%282%29-sqrt%281%29%29%2B%28sqrt%283%29-sqrt%282%29%29%2B%28sqrt%284%29-sqrt%283%29%29%29+=+5%2A%28sqrt%284%29-sqrt%281%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can see that the terms with sqrt(2) and sqrt(3) cancelled, leaving only sqrt(4) and sqrt(1).<br><BR>\n" );
document.write( "The last term in the series is going to be equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28sqrt%2836%29-sqrt%2835%29%29 ALIGN=MIDDLE  ALT=\"5%2A%28sqrt%2836%29-sqrt%2835%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Can you see what you are going to be left with when you add all the terms of the series and cancel where possible?\r<BR>\n" );
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