document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023304>Question 1023304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that 0,3 < S < 0,4 <BR>\n" );
document.write( "S= 1/(1*4) + 1/(4*7) + 1/(7*10) + ... + 1/(2014*2017) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638817 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%281-1%2F4%29%2B%281%2F3%29%281%2F4-1%2F7%29%2B%281%2F3%29%281%2F7-1%2F10%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%281-1%2F4%29%2B%281%2F3%29%281%2F4-1%2F7%29%2B%281%2F3%29%281%2F7-1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%281%2F2011-1%2F2014%29+%2B+%281%2F3%29%281%2F2014-1%2F2017%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%281%2F2011-1%2F2014%29+%2B+%281%2F3%29%281%2F2014-1%2F2017%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >*(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+1%2F4+%2B+1%2F4+-+1%2F7+%2B+1%2F7+-+1%2F10 ALIGN=MIDDLE  ALT=\"1+-+1%2F4+%2B+1%2F4+-+1%2F7+%2B+1%2F7+-+1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2011-1%2F2014+%2B+1%2F2014-1%2F2017 ALIGN=MIDDLE  ALT=\"1%2F2011-1%2F2014+%2B+1%2F2014-1%2F2017\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%281-1%2F2017%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%281-1%2F2017%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = S\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=+%281%2F3%29%282016%2F2017%29+=+672%2F2017+ ALIGN=MIDDLE  ALT=\"S=+%281%2F3%29%282016%2F2017%29+=+672%2F2017+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 0.333168... >0.3, and also \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%281%2F3%29%282016%2F2017%29+%3C+1%2F3+=+0.33333 ALIGN=MIDDLE  ALT=\"S+=+%281%2F3%29%282016%2F2017%29+%3C+1%2F3+=+0.33333\"   DISABLED_style= \"max-width:90%; height:auto;\" >....< 0.4\r<BR>\n" );
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document.write( "Hence,\r<BR>\n" );
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document.write( "0.3 < S < 0.4. </SPAN>\n" );
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