the height a ball bounces is less than the height of the previous bounce due to friction. the heights of the bounces form a geometric sequence. suppose a ball is dropped from one meter and rebounds to 95% of the height of the previous bounce. what is the total distance traveled by the ball when it comes to rest? does the problem give you enough info to solve the problem? how can you write the general term of the sequence? what formula should you use to calculate the total distance?

Question

anonymous · Answer

The equation for the height of the ball after each bounce:
$$h(x_{n})=.95*h(x_{n-1})$$
We refer to this as recursive notation. 
Since we know that
$$h(0)=1\text{ metre}$$
We can use this to find the answer in summation notation.
$$\sum_{x=0}^{\infty}.95^x$$
We then change it to a limit
$$\lim_{x\rightarrow\infty}\sum.95^x$$
See if you can take it from here.