document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=393636>Question 393636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the series 64,-32,16,-8 find:<BR>\n" );
document.write( "i)The tenth term<BR>\n" );
document.write( "ii)the sum of the first 20 terms<BR>\n" );
document.write( "iii)the sum to infinity<BR>\n" );
document.write( "Please help I have already done the first two questions with the results of:<BR>\n" );
document.write( "i)0.0625<BR>\n" );
document.write( "ii)-127.99 (rounded)<BR>\n" );
document.write( "But I am stumped for the third question. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279904 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ratio between two successive terms is -1/2 which is between -1 and 1 so the series converges.\r<BR>\n" );
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document.write( "We have the sum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%2864%2A%28-1%2F2%29%5Er%2C+r+=+0%2C+infinity%29 ALIGN=MIDDLE  ALT=\"sum%2864%2A%28-1%2F2%29%5Er%2C+r+=+0%2C+infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Factoring 64 out, this is equivalent to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64sum%28%28-1%2F2%29%5Er%2C+r+=+0%2C+infinity%29 ALIGN=MIDDLE  ALT=\"64sum%28%28-1%2F2%29%5Er%2C+r+=+0%2C+infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The sum of all the terms of a convergent geometric sequence 1 + r + r^2 + ... = 1/(1-r), so replacing r with -1/2,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64sum%28%28-1%2F2%29%5Er%2C+r+=+0%2C+infinity%29+=+64%2A%281%2F%281-%28-1%2F2%29%29%29+=+64%2A%282%2F3%29+=+128%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that the words \"series\" and \"sequence\" have different meanings. {64, -32, 16, -8, ...} is a sequence. The sum of the terms in a sequence is defined as a series. </SPAN>\n" );
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