document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198602>Question 1198602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sumΣ between n=1 and infinity  for the expression 2(1/3)^n-1.\r<BR>\n" );
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document.write( "The correct answer is one of the following.  Which one. \r<BR>\n" );
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document.write( "A) 3\r<BR>\n" );
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document.write( "B) 3/2\r<BR>\n" );
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document.write( "C) 6\r<BR>\n" );
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document.write( "D) 4/3\r<BR>\n" );
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document.write( "E) 4\r<BR>\n" );
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document.write( "F) does not exist  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832218 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</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=832218\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I believe that your sequence/expression is  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%281%2F3%29%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"2%2A%281%2F3%29%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is the only reasonable version for this context. \r<BR>\n" );
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document.write( "Then the sequence is an infinite geometric progression with the first term of 2\r\n" );
document.write( "and the common ratio  r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "Use the standard formula for the sum of an infinite geometric sequence\r\n" );
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document.write( "    S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "In your case, it gives  S = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%281-1%2F3%29 ALIGN=MIDDLE  ALT=\"2%2F%281-1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28%282%2F3%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28%282%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.    <U>ANSWER</U>\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "--------------\r<BR>\n" );
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document.write( "In the future, use parentheses in your formulas, to show upper indexes ,\r<BR>\n" );
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document.write( "numerators and denominators for clear writing/reading.\r<BR>\n" );
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document.write( "In you case, the expression should be written in this form  2(1/3)^(n-1),\r<BR>\n" );
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document.write( "where the upper index (the degree) goes in parentheses.\r<BR>\n" );
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document.write( "Otherwise, tutors will have difficulties reading/interpreting your posts.\r<BR>\n" );
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