document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472498>Question 472498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sum of the first 20 terms of the series\r<BR>\n" );
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document.write( "1+3+9+27...\r<BR>\n" );
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document.write( "Please explain with a formula. 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 #324698 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I will show you the formula plus how it is derived so that you don't blindly memorize it. Blindly memorizing formulas is a common pitfall students make, and it makes students less likely to actually \"understand\" the material.\r<BR>\n" );
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document.write( "Let\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE S = \sum_{i=0}^{19} 3^i = 3^0+3^1+3^2+...3^{19}\">\r<BR>\n" );
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document.write( "Then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3S = \sum_{i=0}^{19} 3^{i+1} = 3^1 + 3^2 + ... + 3^{20}\">\r<BR>\n" );
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document.write( "We can do 3S - S and obtain lots of cancellation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3S - S = 2S = 3^{20} - 3^0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE S = \frac{3^{20} - 1}{2}\">\r<BR>\n" );
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document.write( "To generalize, you would let the common difference be something like \"r\" then the denominator of 2 would be replaced with r-1. Also, for an arbitrary exponent n (here n = 19) the 20 would be replaced with n+1. </SPAN>\n" );
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