document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763244>Question 763244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > satisfies following condition.<BR>\n" );
document.write( "Calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28+x-%3Einfinity%2C+a%5Bn%5D+%29 ALIGN=MIDDLE  ALT=\"lim%28+x-%3Einfinity%2C+a%5Bn%5D+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=3 ALIGN=MIDDLE  ALT=\"a%5B1%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=%282%2F3%29%2Aa%5Bn%5D+%2B+%281%2F4%29 ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=%282%2F3%29%2Aa%5Bn%5D+%2B+%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (n=1,2,3...) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464661 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=464661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's assume that in the limit (a sub n) becomes a constant value c. then we have<BR>\n" );
document.write( "(1) c = (2/3)*c + (1/4) or<BR>\n" );
document.write( "(2) (1-2/3)*c = 1/4 or<BR>\n" );
document.write( "(3) (1/3)*c = 1/4 or<BR>\n" );
document.write( "(4) c = 3*(1/4) or<BR>\n" );
document.write( "(5) c = 3/4 voila!!!<BR>\n" );
document.write( "Check it<BR>\n" );
document.write( "Is (3/4 = (2/3)*(3/4) + 1/4)?<BR>\n" );
document.write( "Is (3/4 = 1/2 + 1/4)?<BR>\n" );
document.write( "Is (3/4 = 3/4)? Yes<BR>\n" );
document.write( "Answer: In the limit as n goes to infinity a sub n goes to 3/4. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );