document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250559>Question 250559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with my Algebra please. It says tell whether each sequence is convergent or divergent. If it is convergent find it sum.\r<BR>\n" );
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document.write( "1. infinite E (2/3)^n n=0\r<BR>\n" );
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document.write( "2. infinite E (-4/11)^n n=0\r<BR>\n" );
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document.write( "3. infinite E (5^k+1)/3^k n=0\r<BR>\n" );
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document.write( "4. infinite E (3^n-1)/4^n n=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182502 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=182502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hint: Recall that the series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28a%2Ar%5En%2Cn=0%2Cinfinity%29 ALIGN=MIDDLE  ALT=\"sum%28a%2Ar%5En%2Cn=0%2Cinfinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is convergent if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28r%29%3C1 ALIGN=MIDDLE  ALT=\"abs%28r%29%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it diverges otherwise. If it converges, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28a%2Ar%5En%2Cn=0%2Cinfinity%29=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"sum%28a%2Ar%5En%2Cn=0%2Cinfinity%29=a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So for the first problem, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ar%5En=%282%2F3%29%5En ALIGN=MIDDLE  ALT=\"a%2Ar%5En=%282%2F3%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > which makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   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;\" >. Because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28r%29=abs%282%2F3%29%3C1 ALIGN=MIDDLE  ALT=\"abs%28r%29=abs%282%2F3%29%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%282%2F3%29%5En%2Cn=0%2Cinfinity%29=1%2F%281-2%2F3%29=1%2F%281%2F3%29=3 ALIGN=MIDDLE  ALT=\"sum%28%282%2F3%29%5En%2Cn=0%2Cinfinity%29=1%2F%281-2%2F3%29=1%2F%281%2F3%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Use the same idea for the rest of the problems. </SPAN>\n" );
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