document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106812>Question 1106812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of the first ten terms of the geometric series 2-1+½-¼+... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721806 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I personally don't like the formula for the sum of a finite geometric series; for most problems of this type I just do the arithmetic, if the numbers make it practical.<br><BR>\n" );
document.write( "Since this is an alternating series, it simplifies things to group the terms in pairs.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1=1 ALIGN=MIDDLE  ALT=\"2-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2-1%2F4+=+1%2F4 ALIGN=MIDDLE  ALT=\"1%2F2-1%2F4+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; etc.<br><BR>\n" );
document.write( "So the sum of 10 terms of the given geometric series is the sum of 5 terms of this new geometric series:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+1%2F4+%2B+1%2F16+%2B+1%2F64+%2B+1%2F256 ALIGN=MIDDLE  ALT=\"1+%2B+1%2F4+%2B+1%2F16+%2B+1%2F64+%2B+1%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28256%2B64%2B16%2B4%2B1%29%2F256 ALIGN=MIDDLE  ALT=\"%28256%2B64%2B16%2B4%2B1%29%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=341%2F256 ALIGN=MIDDLE  ALT=\"341%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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