document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970720>Question 970720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to learn how to tell the difference between converge and diverge </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593377 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> converge means to come together.<BR>\n" );
document.write( "diverge means to spread apart.\r<BR>\n" );
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document.write( "when a solution converges, it means it is approaching a specific value.\r<BR>\n" );
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document.write( "it is converging to that value.\r<BR>\n" );
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document.write( "when a solution diverges, it means it is getting further and further away from a specific value.\r<BR>\n" );
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document.write( "if you look at a geometric progression, the solution will diverge if r is greaster than 1 and the solution will converge if the r is less then 1 and greater than 0.\r<BR>\n" );
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document.write( "here's a geometric progression when r is greater than 1.\r<BR>\n" );
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document.write( "the formula is y = 10 * 1.5^x.\r<BR>\n" );
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document.write( "as x increases, y increases as well, so the solution is diverging because it is not going towards any specific value.\r<BR>\n" );
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document.write( "here's the same equation where r is less than 1.\r<BR>\n" );
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document.write( "the formula is y = 10000 * .5^x\r<BR>\n" );
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document.write( "you can see that, as x gets larger, the value of y gets closer and closer to 0.\r<BR>\n" );
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document.write( "the solution is converging on 0.\r<BR>\n" );
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