document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407934>Question 407934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of the infinite geometric series 64+48+36+27+...If it has one. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287705 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=287705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This sum is represented in sigma notation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Asum%28%282%2F3%29%5Ei%2C+i+=+0%2C+infinity%29 ALIGN=MIDDLE  ALT=\"64%2Asum%28%282%2F3%29%5Ei%2C+i+=+0%2C+infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If you know that an infinite geometric series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28ar%5Ei%2C+i+=+0%2C+infinity%29 ALIGN=MIDDLE  ALT=\"sum%28ar%5Ei%2C+i+=+0%2C+infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > converges if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C+r+%3C+1 ALIGN=MIDDLE  ALT=\"-1+%3C+r+%3C+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we conclude that the series converges to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+64 ALIGN=MIDDLE  ALT=\"a+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+2%2F3 ALIGN=MIDDLE  ALT=\"r+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Asum%28%282%2F3%29%5Ei%2C+i+=+0%2C+infinity%29+=+64%2F%281+-+%282%2F3%29%29+=+192 ALIGN=MIDDLE  ALT=\"64%2Asum%28%282%2F3%29%5Ei%2C+i+=+0%2C+infinity%29+=+64%2F%281+-+%282%2F3%29%29+=+192\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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