document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118204>Question 1118204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 10. Evaluate the following. Show your work using concepts from this unit.\r<BR>\n" );
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document.write( "a) 1 - 3 + 5 - 7 + 9 -11 + ... + 201 - 203\r<BR>\n" );
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document.write( "b) 300 - 299 + 298 - 297 + ... + 100 - 99 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733465 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "a) 1 - 3 + 5 - 7 + 9 -11 + ... + 201 - 203\r<BR>\n" );
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document.write( "Group the numbers in pairs, using parentheses:\r\n" );
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document.write( "    1 - 3 + 5 - 7 + 9 -11 + ... + 201 - 203 = \r\n" );
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document.write( "  = (1-3) + (5-7) + (9-11) + . . + (201-203) = \r\n" );
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document.write( "  =  -2   +  (-2)   + (-2) + . . . + (-2) = 51 times (-2) = 51*(-2) = -102.\r\n" );
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document.write( "b) 300 - 299 + 298 - 297 + ... + 100 - 99  \r<BR>\n" );
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document.write( "The same idea works:  Group the numbers in pairs, using parentheses\r\n" );
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document.write( "    300 - 299 + 298 - 297 + . . . +  100 - 99  = \r\n" );
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document.write( "  = (300-299) + (298-297) + . . .  + (100-99) =\r\n" );
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document.write( "  =    1     +     1     + . . . +     1     =  101 times 1 = 101*1 = 101.\r\n" );
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document.write( "Actually, &nbsp;this problem is typical one of Math circles for students who are interested in Math.\r<BR>\n" );
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document.write( "These students might be of 5-6-7 grades, &nbsp;who formally don't know arithmetic progressions yet, &nbsp;but have a curious and active mind.\r<BR>\n" );
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document.write( "It is also good as an entertainment problem for aged people, &nbsp;who just forgot long time ago what an arithmetic progression is <BR>\n" );
document.write( "(or even never knew it !), &nbsp;but (again !) have a curious and active mind.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; * * * Good training tool for any age's person who does care about healthiness of his &nbsp;(or her)&nbsp; mind. * * * \r<BR>\n" );
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document.write( " </SPAN>\n" );
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