document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54783>Question 54783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function is written in long form to describe a visual branching problem-- a center star with three points, each of those branching to three points, etc. \r<BR>\n" );
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document.write( "For n=1, total points (x) = 1<BR>\n" );
document.write( "For n=2, total points (x) = 1 + 3\r<BR>\n" );
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document.write( "For n=3, x = 1 + 3 + 3 squared<BR>\n" );
document.write( "For n=4, x = 1 +3 + 3square + 3 cubed<BR>\n" );
document.write( "So the last number in the sequence is always 3 with an exponent of (n-1)\r<BR>\n" );
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document.write( "Short of brute force with a calculatorm how would I calculate x for n=100?<BR>\n" );
document.write( "How would I write the formula? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37194 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=37194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For n=4, x = 1 +3 + 3square + 3 cubed<BR>\n" );
document.write( "So the last number in the sequence is always 3 with an exponent of (n-1) <BR>\n" );
document.write( "Short of brute force with a calculatorm how would I calculate x for n=100?<BR>\n" );
document.write( "How would I write the formula?<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Notice this pattern:<BR>\n" );
document.write( "(1-x^2)/(1-x)=1+x<BR>\n" );
document.write( "(1-x^3)/(1-x)=1+x+x^2<BR>\n" );
document.write( "(1-x^4)/(1-x)=1+x+x^2+x^3<BR>\n" );
document.write( "...<BR>\n" );
document.write( "...<BR>\n" );
document.write( "(1-x^101)/(1-x)= 1+x+x^2+....+x^100<BR>\n" );
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document.write( "So, let x=3<BR>\n" );
document.write( "1+3+3^2+3^3+...+3^100= (1-3^101)/(1-3)<BR>\n" );
document.write( "(1-3^101)/(1-3)= -1.54613256x10^48/-2=7.73066281x10^47<BR>\n" );
document.write( "The formula is the last line with the x's.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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