document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027346>Question 1027346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let n be a positive integer, k the number of prime numbers less than or equal to n, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5Bk%5D ALIGN=MIDDLE  ALT=\"p%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > the greatest prime number less than or equal to n. Prove that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fp%5B1%5D%2B1%2Fp%5B2%5D%2B1%2Fp%5B3%5D ALIGN=MIDDLE  ALT=\"1%2Fp%5B1%5D%2B1%2Fp%5B2%5D%2B1%2Fp%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fp%5Bk-1%5D%2B1%2Fp%5Bk%5D+%3E+%282n%29%2F%28n%2B1%29 ALIGN=MIDDLE  ALT=\"1%2Fp%5Bk-1%5D%2B1%2Fp%5Bk%5D+%3E+%282n%29%2F%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D ALIGN=MIDDLE  ALT=\"p%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D ALIGN=MIDDLE  ALT=\"p%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B3%5D ALIGN=MIDDLE  ALT=\"p%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ...,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5Bk-1%5D ALIGN=MIDDLE  ALT=\"p%5Bk-1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5Bk%5D ALIGN=MIDDLE  ALT=\"p%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the k prime numbers less than or equal to n. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643795 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=643795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is that even true?\r<BR>\n" );
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document.write( "For example, if n = 10, then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} > \frac{20}{11}\">\r<BR>\n" );
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document.write( "which is a false statement. </SPAN>\n" );
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