document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56961>Question 56961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone, please, explain why this equation is true?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+%28-1%29%5Ek+%2A+%28matrix+%282%2C+1%2C+n%2C+k%29%29%2C+k=0%2C+n%29+=+0 ALIGN=MIDDLE  ALT=\"sum%28+%28-1%29%5Ek+%2A+%28matrix+%282%2C+1%2C+n%2C+k%29%29%2C+k=0%2C+n%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I intuitively understand why it works for odd n (as combinations with k elements are as many as combinations with n-k elements and they just cancel each other out in the end). But this doesn't explain the equation for even n.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38707 by </B><A HREF=/tutors/aboutme.mpl?userid=fanks><B>fanks(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fanks><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=38707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Thanks for the reply, Stan!\r<BR>\n" );
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document.write( "However, they don't cancel each out, as, for example, both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix+%282%2C+1%2C+8%2C+6%29%29 ALIGN=MIDDLE  ALT=\"%28matrix+%282%2C+1%2C+8%2C+6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix+%282%2C+1%2C+8%2C+8-6%29%29 ALIGN=MIDDLE  ALT=\"%28matrix+%282%2C+1%2C+8%2C+8-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > would have a plus sign in that sum (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E6 ALIGN=MIDDLE  ALT=\"%28-1%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >). </SPAN>\n" );
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