document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141070>Question 141070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that if the sum of an arithmetic series with an odd number of terms is 0, then one of the terms of the series must be 0. (Hint: let the number of terms be 2k + 1. Show that a1 = -kd. Then find the (k + 1)st term.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102745 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=102745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look here for some hints http://en.wikipedia.org/wiki/Arithmetic_progression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+n%28+2a%5B1%5D+%2B+%28n-1%29d+%29%2F+2+ ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+n%28+2a%5B1%5D+%2B+%28n-1%29d+%29%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Let the number of terms be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k%2B1 ALIGN=MIDDLE  ALT=\"2k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+n%28+2a%5B1%5D+%2B+%282k%2B1-1%29d+%29%2F+2+ ALIGN=MIDDLE  ALT=\"0+=+n%28+2a%5B1%5D+%2B+%282k%2B1-1%29d+%29%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+n%28+2a%5B1%5D+%2B+%282k%29d+%29%2F+2+ ALIGN=MIDDLE  ALT=\"0+=+n%28+2a%5B1%5D+%2B+%282k%29d+%29%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+n%28+a%5B1%5D+%2B+%28k%29d+%29+ ALIGN=MIDDLE  ALT=\"0+=+n%28+a%5B1%5D+%2B+%28k%29d+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-kd = a[1]\r<BR>\n" );
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document.write( "Now the function for the n[th] term of series is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+-kd+%2B+%28n+-+1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+-kd+%2B+%28n+-+1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+%28n+-+1+-k%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+%28n+-+1+-k%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%2B1%5D+++=+%28k+%2B1+-+1+-k%29d ALIGN=MIDDLE  ALT=\"a%5Bk%2B1%5D+++=+%28k+%2B1+-+1+-k%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%2B1%5D+++=+%280%29d ALIGN=MIDDLE  ALT=\"a%5Bk%2B1%5D+++=+%280%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bk%2B1%5D+=+0 ALIGN=MIDDLE  ALT=\"a%5Bk%2B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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