document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537595>Question 537595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> EVALUATE:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B3%2F4%2B7%2F16%2B15%2F64%2B31%2F256 ALIGN=MIDDLE  ALT=\"1%2B3%2F4%2B7%2F16%2B15%2F64%2B31%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......... to infinity </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352942 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=352942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B3%2F4%2B7%2F16%2B15%2F64%2B31%2F256 ALIGN=MIDDLE  ALT=\"1%2B3%2F4%2B7%2F16%2B15%2F64%2B31%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......... to infinity<BR>\n" );
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document.write( "Consider the first term as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1%2B3%2F4%2B7%2F16%2B15%2F64%2B31%2F256 ALIGN=MIDDLE  ALT=\"1%2F1%2B3%2F4%2B7%2F16%2B15%2F64%2B31%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" > ......... to infinity<BR>\n" );
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document.write( "The numerators form the sequence 1,3,7,15,31 <BR>\n" );
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document.write( "That has nth term<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-1 ALIGN=MIDDLE  ALT=\"2%5En-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The denominators form the sequence 1,4,16,64,256 <BR>\n" );
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document.write( "That has nth term<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"2%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore the sequence summed to infinity is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28++%28%282%5En-1%29%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29 ALIGN=MIDDLE  ALT=\"sum%28++%28%282%5En-1%29%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28++%28%282%5En%29%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29 ALIGN=MIDDLE  ALT=\"sum%28++%28%282%5En%29%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28++%281%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29 ALIGN=MIDDLE  ALT=\"sum%28++%281%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
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document.write( "Subtract exponents in the first:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28++%282%5E1%29%2Cn=1%2Cinfinity+%29 ALIGN=MIDDLE  ALT=\"sum%28++%282%5E1%29%2Cn=1%2Cinfinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28++%281%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29 ALIGN=MIDDLE  ALT=\"sum%28++%281%2F%282%5E%28n-1%29%29%29%2Cn=1%2Cinfinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first series diverges to infinity and the second one is a geometric<BR>\n" );
document.write( "series converging to 2, so the series diverges to infinity.<BR>\n" );
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document.write( "Edwin</pre>  </SPAN>\n" );
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