# Sum sequence of a geometric series

1. Jun 22, 2012

### thekopite

1. The problem statement, all variables and given/known data

A 'supa-ball' is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing?

2. Relevant equations

3. The attempt at a solution

The consecutive heights which the ball attains form a geometric series with first term a=1 and common ratio 0.9. Using the formula for the sum to infinity of the series, I am left with S = a/(1-r) = 1/0.1 = 10 metres
However, the answer given is 19 metres. I don't understand how to get to this answer, is this just a typo?

2. Jun 22, 2012

### Infinitum

Hi thekopite! Welcome to PF

When the ball moves up 0.9h, it also comes down. You need to include that in your answer

3. Jun 22, 2012

### Millennial

Each bounce of the ball has an identical coming down length. For example, if the ball bounces 0.9 metres, it will also come down 0.9 metres, travelling a total distance of 1.8 metres.

4. Jun 22, 2012

### Infinitum

Exactly....Except the first 1m fall

Edit : Oops...I thought the OP posted.:uhh:

5. Jun 22, 2012

### thekopite

thanks, i get it know. feeling a little dumb.