document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=809009>Question 809009</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The sum\r<BR>\n" );
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document.write( "1 - 2 + 3 - 4 + ... + 65 - 66 + 67\r<BR>\n" );
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document.write( "is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #487358 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=487358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1 - 2 + 3 - 4 + ... + 65 - 66 + 67\r<BR>\n" );
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document.write( "let us break it up into two sequences\r<BR>\n" );
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document.write( "both are arithmetic progressions\r<BR>\n" );
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document.write( "1+3+5..........67\r<BR>\n" );
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document.write( "a=1,d=2 Tn=67\r<BR>\n" );
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document.write( "67=1+(n-1)2<BR>\n" );
document.write( "67=1+2n-2<BR>\n" );
document.write( "2n=68<BR>\n" );
document.write( "n=34\r<BR>\n" );
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document.write( "Sn = n/2(2a+(n-1)d)<BR>\n" );
document.write( "=(34/2(2*1+(37-1)2)<BR>\n" );
document.write( "=17*(2+36*2)<BR>\n" );
document.write( "=17*74<BR>\n" );
document.write( "=1258\r<BR>\n" );
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document.write( "and -2,-4,-6......-66\r<BR>\n" );
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document.write( "a=-2, d=-2 Tn= -66\r<BR>\n" );
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document.write( "-66=-2+(n-1)*-2\r<BR>\n" );
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document.write( "-66=-2-2n+2\r<BR>\n" );
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document.write( "n=33\r<BR>\n" );
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document.write( "S33= 33/2( 2*-2+(33-1)*-2)\r<BR>\n" );
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document.write( "S33=33/2(-4-64)\r<BR>\n" );
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document.write( "S33=33/2 * -68\r<BR>\n" );
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document.write( "=33*-34<BR>\n" );
document.write( "=-1122\r<BR>\n" );
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document.write( "1258-1122\r<BR>\n" );
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document.write( "=136 </SPAN>\n" );
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