None of the following experiments can be carried out in practice.

But that doesn't stop us from thinking about them.

In one way or another each of them involves the infinite series

1/2 + 1/4 + 1/8 + ... + = 1.

Each asks for a response. Which responses, if any, can be given?

A lamp is switched on and remains on for 1/2 minute.
Then it's switched off for 1/4 minute.
Then on for 1/8 minute, and so on.
After 1 minute, of course, the switching stops.
Describe the condition [on or off] of the lamp. .

A supercomputer is programmed to calculate a print the value of pi, one digit at at time.
The first digit prints after 1/2 minute. Each succeeding digit prints in 1/2 the time, and,
[to keep the supply of printer paper finite], in 1/2 the space of the previous digit.
After 1 minute, of course, the printing stops.
Can we at last determine pi's final digit? .

A marble rests in tray A.
After 1/4 minute a machine transfers the marble to tray B and rests for another
1/4 minute while a different machine transfers the marble back to tray A.
During the next 1/8 minute the first machine puts the marble back to tray B
and rests 1/8 minute while the second machine returns it to tray A.
After 1 minute the halved-time transferring process stops.
Describe the location [tray A or B] of the marble. .

A constant-speed runner completes 1/2 of his journey in 1/4 minute; then he rests for 1/4 minute.
In the next 1/8 minute he completes 1/4 of his journey, resting thereafter for 1/8 minute. And so on.
Describe the position of the runner after 1 minute. .

A certain toy ball returns to 1/2 its original height 1/2 minute after being dropped.
It falls from that point and returns to 1/4 the original height 1/4 minute later,
and to 1/8 the height 1/8 minute after that. And so on.
Describe the motion of the ball 1 minute after the initial drop. .

The ball in question 5 is initially red.
It changes color, alternating between red and blue, each time it strikes the ground.
Describe its color after 1 minute. .

## Question

## bonanova 84

None of the following experiments can be carried out in practice.

But that doesn't stop us from thinking about them.

In one way or another each of them involves the infinite series

1/2 + 1/4 + 1/8 + ... + = 1.

Each asks for a response. Which responses, if any, can be given?

Then it's switched off for 1/4 minute.

Then on for 1/8 minute, and so on.

After 1 minute, of course, the switching stops.

Describe the condition [on or off] of the lamp.

.

The first digit prints after 1/2 minute. Each succeeding digit prints in 1/2 the time, and,

[to keep the supply of printer paper finite], in 1/2 the space of the previous digit.

After 1 minute, of course, the printing stops.

Can we at last determine pi's final digit?

.

After 1/4 minute a machine transfers the marble to tray B and rests for another

1/4 minute while a different machine transfers the marble back to tray A.

During the next 1/8 minute the first machine puts the marble back to tray B

and rests 1/8 minute while the second machine returns it to tray A.

After 1 minute the halved-time transferring process stops.

Describe the location [tray A or B] of the marble.

.

In the next 1/8 minute he completes 1/4 of his journey, resting thereafter for 1/8 minute. And so on.

Describe the position of the runner after 1 minute.

.

It falls from that point and returns to 1/4 the original height 1/4 minute later,

and to 1/8 the height 1/8 minute after that. And so on.

Describe the motion of the ball 1 minute after the initial drop.

.

It changes color, alternating between red and blue, each time it strikes the ground.

Describe its color after 1 minute.

.

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