document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305226>Question 305226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the sum of infinite geometric series? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218557 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=218557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you find the sum of infinite geometric series?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "S(n) = a + ar + ar^2 +...+ar^(n-1)<BR>\n" );
document.write( "r*S(n) =   ar + ar^2 + ..+ar^(n-1)+ ar^n<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Subtract the 2nd line from the 1st to get:<BR>\n" );
document.write( "S(n) - r*S(n) = a -ar^n<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Factor both sides and solve for S(n):<BR>\n" );
document.write( "S(n)*(1-r) = a(1-r^n)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "S(n) = [a(1-r^n)/(1-r)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If 0< r < 1 and n goes to infinity, r^n goes to zero<BR>\n" );
document.write( "and you get:<BR>\n" );
document.write( "S(n) = a/(1-r)<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );