document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=929347>Question 929347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve the following: determine whether the infinite geometric series converges or diverges. Find its sum<BR>\n" );
document.write( "5-5/3+5/9-5/27+... thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #564252 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=564252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The initial term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B0%5D+=+5 ALIGN=MIDDLE  ALT=\"a%5B0%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The common ration is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ar=-5%2F3 ALIGN=MIDDLE  ALT=\"5%2Ar=-5%2F3\"   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=r=-%285%2F3%29%2F5 ALIGN=MIDDLE  ALT=\"r=-%285%2F3%29%2F5\"   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=r=-5%2F15 ALIGN=MIDDLE  ALT=\"r=-5%2F15\"   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=r=-1%2F3 ALIGN=MIDDLE  ALT=\"r=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: that the common ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-1%2F3 ALIGN=MIDDLE  ALT=\"r+=+-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28r%29+%3C+1 ALIGN=MIDDLE  ALT=\"abs%28r%29+%3C+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we know that the infinite geometric series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=converges ALIGN=MIDDLE  ALT=\"converges\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28-5%28-1%2F3%29%5En%29%2Cn=1%2Cinfinity%29+=a%5B0%5D%2A%28r%2F%281-r%29%29%0D%0A%0D%0A-5%2A%28%28-1%2F3%29%2F%281-%28-1%2F3%29%29%29+=+-5%2A%28%28-1%2F3%29%2F%284%2F3%29%29+=+5%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so the series converges and has a sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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