document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486729>Question 486729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q1) 11,38,136,?.... what will be the next tram?<BR>\n" );
document.write( "Q2) S= root1+ root2+ root3+.....+root10000 what value of S? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332752 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332752\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q1: There is no distinguishable pattern for that sequence; there could be several possible next terms.\r<BR>\n" );
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document.write( "Q2: Finding the exact sum would be extremely difficult without using a calculator or computer; however you can approximate that sum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{k=1}^{10000} \sqrt{k} \approx \int_{0}^{10000} \sqrt{x}\,dx\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = \frac{2}{3} (10000)^{\frac{3}{2}} - \frac{2}{3} (0)^{\frac{3}{2}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = \frac{2}{3}(10^6) = 666667\">\r<BR>\n" );
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document.write( "Wolfram Alpha says that the sum is about 666716, so this is a good approximation (we know we are under because the sum uses the right endpoints, so the sum would be slightly higher than the integral value). </SPAN>\n" );
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