document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856666>Question 856666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that (n+1)!-3(n!)+(n-1)!=(n-1)!(n-1)^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516104 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=516104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Keep in mind that n! = n*(n-1)*(n-2)...(3)*(2)*(1)\r<BR>\n" );
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document.write( "You can shorten this to say n! = n(n-1)!\r<BR>\n" );
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document.write( "Similarly, (n+1)! = (n+1)*n! which leads to (n+1)! = (n+1)*n*(n-1)!\r<BR>\n" );
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document.write( "We'll use these equations to make substitutions below\r<BR>\n" );
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document.write( "(n+1)!-3(n!)+(n-1)!=(n-1)!(n-1)^2\r<BR>\n" );
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document.write( "(n+1)*(n)*(n-1)!-3(n)*(n-1)!+(n-1)!=(n-1)!(n-1)^2\r<BR>\n" );
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document.write( "(n-1)! [ (n+1)*(n)-3(n)+1 ] = (n-1)!(n-1)^2\r<BR>\n" );
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document.write( "(n-1)! [ n^2+n-3n+1 ] = (n-1)!(n-1)^2\r<BR>\n" );
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document.write( "(n-1)! [ n^2-2n+1 ] = (n-1)!(n-1)^2\r<BR>\n" );
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document.write( "(n-1)! (n-1)^2 = (n-1)!(n-1)^2\r<BR>\n" );
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document.write( "So the identity is confirmed.\r<BR>\n" );
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document.write( "Notice how I only changed the left side and didn't alter the right side. </SPAN>\n" );
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