document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176165>Question 1176165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For which values of x will \r<BR>\n" );
document.write( "\n" );
document.write( "(-3x+5/2)+(-3x+5/2)²+(-3+5/2)³+....\r<BR>\n" );
document.write( "\n" );
document.write( "be a converging series? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #802440 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=802440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A geometric series will converge whenever the common ratio is between -1 and 1.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C+-3x%2B5%2F2+%3C+1 ALIGN=MIDDLE  ALT=\"-1+%3C+-3x%2B5%2F2+%3C+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1-5%2F2+%3C+-3x+%3C+1-5%2F2 ALIGN=MIDDLE  ALT=\"-1-5%2F2+%3C+-3x+%3C+1-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F2+%3C+-3x+%3C+-3%2F2 ALIGN=MIDDLE  ALT=\"-7%2F2+%3C+-3x+%3C+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F6+%3E+x+%3E+1%2F2 ALIGN=MIDDLE  ALT=\"7%2F6+%3E+x+%3E+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (switch the direction of the inequality when dividing by a negative)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+%3C+x+%3C+7%2F6 ALIGN=MIDDLE  ALT=\"1%2F2+%3C+x+%3C+7%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The series will converge for any values of x between 1/2 and 7/6.<br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );