document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001038>Question 1001038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does the infinite series diverge or converge? If it converges what is the sum?<BR>\n" );
document.write( "10+2+2/5+2/25+....<BR>\n" );
document.write( "what is <BR>\n" );
document.write( "a_n= 2a_n-1 -1 where a_1 = 2? <BR>\n" );
document.write( "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 #618345 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Does the infinite series diverge or converge? If it converges what is the sum?<BR>\n" );
document.write( "10+2+2/5+2/25+....<BR>\n" );
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document.write( "It is the sum a geometric progression with the first term a = 10 and the common ratio r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This infinite series converges for any geometric progression with the <U>common ratio less than 1 in the modulus</U>.\r<BR>\n" );
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document.write( "The sum of an infinite geometric progression with the first term a and the raio r, |r| < 1, is \r<BR>\n" );
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document.write( "S = <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;\" >.\r<BR>\n" );
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document.write( "In your case S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281+-+%281%2F5%29%29 ALIGN=MIDDLE  ALT=\"10%2F%281+-+%281%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%28%284%2F5%29%29 ALIGN=MIDDLE  ALT=\"10%2F%28%284%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A5%29%2F4 ALIGN=MIDDLE  ALT=\"%2810%2A5%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12.5.\r<BR>\n" );
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document.write( "what is <BR>\n" );
document.write( "a_n= 2a_n-1 -1 where a_1 = 2? <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aa%5B1%5D+-+1 ALIGN=MIDDLE  ALT=\"2%2Aa%5B1%5D+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2*2 - 1 = 3,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D ALIGN=MIDDLE  ALT=\"a%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aa%5B2%5D+-+1 ALIGN=MIDDLE  ALT=\"2%2Aa%5B2%5D+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2*3 - 1 = 5,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D ALIGN=MIDDLE  ALT=\"a%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aa%5B3%5D+-+1 ALIGN=MIDDLE  ALT=\"2%2Aa%5B3%5D+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2*5 - 1 = 9,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D ALIGN=MIDDLE  ALT=\"a%5B5%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aa%5B4%5D+-+1 ALIGN=MIDDLE  ALT=\"2%2Aa%5B4%5D+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2*9 - 1 = 17,\r<BR>\n" );
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document.write( "and so on . . . \r<BR>\n" );
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document.write( "You can easily calculate it yourself.\r<BR>\n" );
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