document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010816>Question 1010816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x-1/2) - (x-2/2) + (x-3/2) - ... - (x-100/2)\r<BR>\n" );
document.write( "\n" );
document.write( "Please have clear steps and working out. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626299 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=626299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The expression has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-n%2F2%29 ALIGN=MIDDLE  ALT=\"%28x-n%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with alternating <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B%22 ALIGN=MIDDLE  ALT=\"%22%2B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22-%22 ALIGN=MIDDLE  ALT=\"%22-%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > signs.<BR>\n" );
document.write( "On removing the brackets, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B+x%22 ALIGN=MIDDLE  ALT=\"%22%2B+x%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22-+x%22 ALIGN=MIDDLE  ALT=\"%22-+x%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms cancel out.<BR>\n" );
document.write( "After taking out the common factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%29 ALIGN=MIDDLE  ALT=\"1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we get a sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > integer terms that can be grouped in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F2=50 ALIGN=MIDDLE  ALT=\"100%2F2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > pairs of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B1%29+-+m=1 ALIGN=MIDDLE  ALT=\"%28m%2B1%29+-+m=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F2%29+-+%28x-2%2F2%29+%2B+%28x-3%2F2%29+-%28x-4%2F2%29%2B+%22...%22%2B%28x-99%2F2%29+-+%28x-100%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2-x%2B2%2F2%2Bx-3%2F2-x%2B4%2F2%2B+%22...%22%2Bx-99%2F2-x%2B100%2F2 ALIGN=MIDDLE  ALT=\"x-1%2F2-x%2B2%2F2%2Bx-3%2F2-x%2B4%2F2%2B+%22...%22%2Bx-99%2F2-x%2B100%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2%2B2%2F2-3%2F2%2B4%2F2-%22...%22-99%2F2%2B100%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2%2B2%2F2-3%2F2%2B4%2F2-%22...%22-99%2F2%2B100%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%28-1%2B2-3%2B4-%22...%22-99%2B100%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A%28-1%2B2-3%2B4-%22...%22-99%2B100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A%28%282-1%29%2B%284-3%29%2B%22...%22%2B%28100-99%29%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A%28%282-1%29%2B%284-3%29%2B%22...%22%2B%28100-99%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A50=highlight%2825%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A50=highlight%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );