document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128932>Question 128932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem:\r<BR>\n" );
document.write( "\n" );
document.write( "How far up and down will a ball travel before stopping if it is dropped from a height of 12m, and each rebound is 1/3 of the previous distance?\r<BR>\n" );
document.write( "\n" );
document.write( "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 #94299 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first it goes down 12mts <BR>\n" );
document.write( "then  it goes up 4 mts (1/3 of 12mts) <BR>\n" );
document.write( "then  it goes down  4 mts  <BR>\n" );
document.write( "then  it goes up  4/3 mts <BR>\n" );
document.write( "then  it goes down  4/3 mts\r<BR>\n" );
document.write( "\n" );
document.write( "so to find the total up and down you have to sum 12+4+4+4/3+4/3....<BR>\n" );
document.write( "12+ 2(4 (1+1/3+1/9+1/27+......)) =12+8(1+1/3+1/9+1/27+....)<BR>\n" );
document.write( "= 12+8(1/(1-1/3))=12+8(3/2)=24 mts\r<BR>\n" );
document.write( "\n" );
document.write( "note that the serie 1+1/3+1/9+1/27+.... is a geometric serie with ratio 1/3 and the sum is 1/(1-1/3)=3/2\r<BR>\n" );
document.write( "\n" );
document.write( "R:24 mts\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );