document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772715>Question 772715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A kangaroo hops in such a way that the distance covered<BR>\n" );
document.write( "in each hop is half that of the previous one. The<BR>\n" );
document.write( "kangaroo started bouncing from a tree and hopped a<BR>\n" );
document.write( "distance of 2 m. on his third hop. How far is the kangaroo<BR>\n" );
document.write( "from the tree after its tenth hop? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471087 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the kangaroo hops <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m on the<BR>\n" );
document.write( "1st hop, each succeeding hop is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2A2%5E%28-n%29+ ALIGN=MIDDLE  ALT=\"+a%2A2%5E%28-n%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0,1,2,3. . . .<BR>\n" );
document.write( "The sum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2A%28+2%5E0+%2B+2%5E%28-1%29+%2B+2%5E%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+a%2A%28+2%5E0+%2B+2%5E%28-1%29+%2B+2%5E%28-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > . . . <BR>\n" );
document.write( "The formula for the geometric sum is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2A%28+1+-+r%5En%29+%2F+%28+1+-+r+%29+ ALIGN=MIDDLE  ALT=\"+a%2A%28+1+-+r%5En%29+%2F+%28+1+-+r+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+r+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+10+ ALIGN=MIDDLE  ALT=\"+n+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+1+-+%28+1%2F2%29%5E10+%29+%2F+%28+1+-+1%2F2+%29++ ALIGN=MIDDLE  ALT=\"+2%2A%28+1+-+%28+1%2F2%29%5E10+%29+%2F+%28+1+-+1%2F2+%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+1+-+1%2F1024+%29+%2F+%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28+1+-+1%2F1024+%29+%2F+%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2A%28+1023%2F1024+%29+ ALIGN=MIDDLE  ALT=\"+4%2A%28+1023%2F1024+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1023%2F256+ ALIGN=MIDDLE  ALT=\"+1023%2F256+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3.9961+ ALIGN=MIDDLE  ALT=\"+3.9961+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The kangaroo is 3.9961 m from the tree\r<BR>\n" );
document.write( "\n" );
document.write( "    </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );