Thread: Series/Convegence tests! need help on review problems for test!

1. A certain ball has the property that each time it falls from a height h onto a hard, level surface, it rebounds to a height rh, where 0 < r < 1. Suppose that the ball is dropped from an initial height of H meters.
a) Assuming the ball bounces indefinitely, find the total distance that it travels (Use the fact that the ball falls 1/2gt^2 meters in t seconds)
b)calculate the total time that the ball travels

2. A series is Sum an is defined by the equations:

a1 = 1 an+1 = [(2+cosn)/(sqrt(n)]*an

Determine whether Sum an converges or diverges.

could someone show me how to do these? going NUTS.
thank u

Hello, xfyz!

I'll get you started on #1 . . .

1. A certain ball has the property that each time it falls from a height
onto a hard, level surface, it rebounds to a height , where
Suppose that the ball is dropped from an initial height of meters.

a) Assuming the ball bounces indefinitely, find the total distance that it travels.

Let's baby-talk our way through the first few bounces . . .


First, it falls meters.

Then it bounces up m . . . and falls m.

Then it bounces up . . . and falls

Then it bounces up . . . and falls

. . and so on . . .


The total distance is: .

. .

The series in paretheses has first term 1 and common ratio
. . Its sum is: .

So we have: .

Originally Posted by xfyz

2. A series is Sum an is defined by the equations:

a1 = 1 an+1 = [(2+cosn)/(sqrt(n)]*an

Determine whether Sum an converges or diverges.

could someone show me how to do these? going NUTS.
thank u

I think is converges.

First note that,
.
Thus,

Use the root test,
because .
Thus, by the comparison test this series converges.