document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=366143>Question 366143</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what name is given to all the numbers that can be expressed as the sum of two consecutive numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260953 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=260953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n = first number (which is an integer)\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the next consecutive number.\r<BR>\n" );
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document.write( "Now add up the two numbers to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B%28n%2B1%29=%28n%2Bn%29%2B1=2n%2B1 ALIGN=MIDDLE  ALT=\"n%2B%28n%2B1%29=%28n%2Bn%29%2B1=2n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since n is an integer, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n ALIGN=MIDDLE  ALT=\"2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is even (since 2 is a factor). So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%2B1 ALIGN=MIDDLE  ALT=\"2n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is odd.\r<BR>\n" );
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document.write( "So any odd number can be expressed as the sum of two consecutive numbers.\r<BR>\n" );
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document.write( "So to answer the question \"what name is given to all the numbers that can be expressed as the sum of two consecutive numbers?\", the answer is the set of odd integers. </SPAN>\n" );
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