document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025317>Question 1025317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that:<BR>\n" );
document.write( " (a1/a2 + a2/a3 + ... + an-1/an + an/a1)>= n<BR>\n" );
document.write( "*a1 , a2 , ... , an-1 , an are not a*1 , a*2 , ... , a*n . They are parameters, or indexes (in the bottom right corner of the number) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640611 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=640611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large a_1, a_2, \ldots, a_n\"> are positive (otherwise the inequality might not hold), then by the AM-GM inequality we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{ \frac{a_1}{a_2} + \frac{a_2}{a_3} + \ldots + \frac{a_n}{a_1}}{n} \ge \sqrt[n]{\frac{a_1}{a_2} \cdot \frac{a_2}{a_3} \cdot \ldots \cdot \frac{a_n}{a_1}}\">\r<BR>\n" );
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document.write( "Right-hand side equals 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large\frac{ \frac{a_1}{a_2} + \frac{a_2}{a_3} + \ldots + \frac{a_n}{a_1}}{n} \ge 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{a_1}{a_2} + \frac{a_2}{a_3} + \ldots + \frac{a_n}{a_1} \ge n\">\r<BR>\n" );
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document.write( "as desired. </SPAN>\n" );
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