Question

Please help me get started with the following infinite-series problem. A ball is dropped from a height of 10m. Each time it strikes the ground it bounces vertically to a height that is 3/4 of the preceding height. Find the total distance the ball will travel if it is assumed to bounce infinitely often.

Answer 1

1) Down 10
2) Up 10*(3/4)
3) Down 10*(3/4)
4) Up 10*(3/4)*(3/4)
5) Down 10*(3/4)*(3/4)
...

Answer 2

d u d u d ...
10 + 10(3/4) + 10(3/4) + 10(3/4)^2 + 10(3/4)^2 + ...

Answer 3

10 ( 3/4 + 3/4 + 3/4^2 + 3/4^2 + 3/4^3 + 3/4^3+ 3/4^4 + 3/4^4+...)

10 ( 2(3/4) + 2(3/4)^2 + 2(3/4)^3 + 2(3/4)^4 + 2(3/4)^5+...)
10(2) ( 3/4 + 3/4^2 + 3/4^3 + 3/4^4 + 3/4^5+...)

Answer 4

i forgot to mention to ignore the first drop :)

add that on afterwards