document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158664>Question 1158664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a ball is dropped from a height of 2 meters and bounces up to 3/4 of its previous height on each bounce. using geometric series, how much TOTAL DISTANCE (up and down) does the ball travel until it stops bouncing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781624 by </B><A HREF=/tutors/aboutme.mpl?userid=Shin123><B>Shin123(626)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Shin123><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=Shin123><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ball keeps bouncing a fraction of its height. The ball in theory never stops bouncing (but in real life, it eventually does). So it is an infinite geometric sequence. <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=geometric_sequence_sum_infinite_2749.solver>Finding Sum of An Infinite Geometric Sequence </A></TD></TR>\n" );
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document.write( " So for an infinite geometric series, the sum of it is always <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S=a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > under the condition that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28r%29%3C1 ALIGN=MIDDLE  ALT=\"abs%28r%29%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In this case, a is 2 and r is 0.75.So the sum of the series is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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