document.write( "Question 1111661: please help me solve this question:a rubber ball is dropped from a height of 10 meters,suppose it rebounds half the distance after each fall,find the total distance the ball travels.
\n" ); document.write( "thank you \n" ); document.write( "
Algebra.Com's Answer #726647 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
The first bounce(s1) it covers 10+(10/2) = 15m.
\n" ); document.write( ":
\n" ); document.write( "The second bounce(s2), it is (10/2)+(10/4) = 7.5m
\n" ); document.write( ":
\n" ); document.write( "The third bounce(s3), it is (10/4)+(10/8) = 3.75m and so forth
\n" ); document.write( ":
\n" ); document.write( "The distance covered by each bounce is 1/2 the distance covered by the previous bounce
\n" ); document.write( ":
\n" ); document.write( "The total distance covered is the sum of the partial sums,
\n" ); document.write( ":
\n" ); document.write( "total distance = s1 + s2 + s3 + ...... + sn
\n" ); document.write( ":
\n" ); document.write( "Note that the partial sums si form a geometric series where the common ratio is 1/2
\n" ); document.write( ":
\n" ); document.write( "si = s1 * (1/2)^(n-1), where i = 1, n
\n" ); document.write( ":
\n" ); document.write( "when the absolute value of the common ratio is less than 1, the sum is defined as
\n" ); document.write( ":
\n" ); document.write( "sum = s1 / (1 - r), where s1 is the initial term and r is the common ratio
\n" ); document.write( ":
\n" ); document.write( "*************************************
\n" ); document.write( "sum = 15 / (1 - (1/2)) = 15 * 2 = 30m
\n" ); document.write( "*************************************
\n" ); document.write( ": \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );