document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485051>Question 485051</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7 people meet and shake hands with one another, how many handshakes occurred?\r<BR>\n" );
document.write( "\n" );
document.write( "using inductive reasoning, wrte a formula for the number of handshakes if the number of people is n.\r<BR>\n" );
document.write( "\n" );
document.write( "the Fibonacci sequence consists of the pattern 1,1,2,3,5,8,13,...., what is the ninth term in the pattern?\r<BR>\n" );
document.write( "\n" );
document.write( "look at the successive ratios of ne term to the next, make a conjecture?\r<BR>\n" );
document.write( "\n" );
document.write( "list the first eight terms of the sequence formed by finding the differences of sucessive terms in the fibonacci sequence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331811 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first of the 7 people will shake hands with 6 others.  Only 6 because no person is going to shake hands with themselves.  The second person also shakes hands with 6 people, but you have already counted one of those handshakes, namely the one with the first person.  Therefore, the second person shakes hands with only 5 NEW people.  Then the third person adds 4 new handshakes, etc., down to the 2nd to the last person who adds 1 new handshake.  The last person has no one new, so all of the last person's handshakes are already counted.  In summary:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6\ +\ 5\ +\ 4\ +\ 3\ +\ 2\ +\ 1\ =\ \frac{7\,\cdot\,6}{2}\ =\ 21\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you have <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> people, then follow the same pattern:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (n\ -\ 1)\ +\ (n\ -\ 2)\ +\ \cdots\ +\ 2\ +\ 1\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or put more succinctly using sigma notation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i\,=\,1}^{n\,-\,1}\ i\ =\ \frac{n(n\,-\,1)}{2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<div  DISABLED_style= \"text-align:center\"><a  rel=nofollow HREF=\"http://outcampaign.org/\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png\" border=\"0\" alt=\"The Out Campaign: Scarlet Letter of Atheism\" width=\"143\" height=\"122\" /></a></div><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );