1. ## Series help!

Okay, There are a few on my homework that i don't understand...

A ball drops from a height of 19 feet. Each time it hits the ground, it bounces up 40 percents of the height it fall. Assume it goes on forever, find the total distance it travels.
i wrote this as a geometric series, with sigma(from n=1 to infinity) of 19*0.4^(n-1), which would then converge to a/1-r = 31.6666, but it's incorrect, is there an error in the way i set it up?

Determine the sum of: sigma(from n=1 to infinity) of (4^(n-1)/8^n)
not sure how to do this!
Also need help with from n=5 to infinity of 7^n/8^n and from n=1 to infinity of (7^n+2^n)/(8^n)

2. Originally Posted by mistykz
Okay, There are a few on my homework that i don't understand...

A ball drops from a height of 19 feet. Each time it hits the ground, it bounces up 40 percents of the height it fall. Assume it goes on forever, find the total distance it travels.
i wrote this as a geometric series, with sigma(from n=1 to infinity) of 19*0.4^(n-1), which would then converge to a/1-r = 31.6666, but it's incorrect, is there an error in the way i set it up?
yes. you only considered the distance traveled in one direction. here you added up the total falling distances. what about the distance traveled when bouncing up?

the rest of your questions are applications of geometric series.
Determine the sum of: sigma(from n=1 to infinity) of (4^(n-1)/8^n)
not sure how to do this!
$\displaystyle \sum \frac {4^{n - 1}}{8^n} = \frac 14 \sum \frac {4^n}{8^n} = \frac 14 \sum \left( \frac 48 \right)^n = \frac 14 \sum \left( \frac 12 \right)^n$. now continue

use the same procedure for the others