I lost my calculator batteries in a flood .

[BobG]

I lost my calculator batteries in a flood...

What's this equal?

$$\left(\frac{256^{16}-1}{256^{16}}\right)^{256^{16}}$$

a) 2.178
b) 1.000
c) .3679
d) 0.000

 

[chroot]

Well, it's obviously not one, because the number inside the parentheses is not one.

It's also obviously not zero for the same reason.

It's not 2.178, because the number inside the parentheses is less than one, and multiplying a fraction smaller than one by another fraction smaller than one must result in a fraction smaller than one.

By the process of elimination, it must be 0.3679.

- Warren

 

[Manu2380]

i get 1/e...i could be missing something in my work...or maybe even forgetting my calculus lol...

y = [(x-1)/x]^x
lny = x[ln(x-1) - lnx]
lny = ln(x-1 / x) / 1/x
using lhopitals...

lny = (x/(x-1))(1/x^2) / -1/x^2
lny = -x/ x-1 as x approaches infinity...lny = -1 so y = 1/e

But i may be wrong since i am assuming x goes to infinity while its 256^16.

Manu

 

[chroot]

As the number x in

$$\left(\frac{x-1}{x}\right)^{x}$$

approaches infinity, the result definitely does approach 1/e. Since 256^16 has plenty of significant digits, 1/e is close enough to an accuracy of only four decimals.

- Warren

 

[Gokul43201]

And that's what 0.3679 is !

 

[Manu2380]

Hi Warren,

im such a dummy, lol, for 1/e in my windows calc. i kept using 2.178 which is answer a) for the constant e. Finally i looked e in my pocket handbook and found the right one, so it is answer c. And btw how did you use equation in the posts? Please do let me know tnx Warren.

Manu

 

[chroot]

https://www.physicsforums.com/showthread.php?t=8997 And btw how did you use equation in the posts? Please do let me know tnx Warren.

The short answer is simply to click on the images to see their source code. You can just copy and paste the source into your own messages to include those equations. You'll figure out how it works in no time by example.

The long answer is to read this thread:

https://www.physicsforums.com/showthread.php?t=8997

- Warren

 

[Gokul43201]

Manu, we have Chroot to thank for LaTex on PF.

 

[BobG]

No one silly enough to unthinkingly punch this in on their calculator, huh?

 

[Gokul43201]

No, i did, i readd tah title adn did the same but i got 0 in the end hmm!

Strange I would have thought you'd get 1

 

[AndrewEskeClarke]

Would it not be d) 0.000 because in the parantheses would be a decimal and therefore as it grew exponentially it would lessen infinitely towards 0, and 0.000 just means that whatever number rounded to three decimal places would be 0? Or did y'all already establish that?

 

[Gaz031]

No one silly enough to unthinkingly punch this in on their calculator, huh?

>_< ..., whistles and looks over shoulder..

 

[Tau_Muon_PlanetEater]

The answer is something like .9999999999999999999999999999999 but has many more nines than i can fit. So this rounds to 1.000, since the answers go to 3 decimals.

That is the answer.

 

[Tau_Muon_PlanetEater]

My mistake, the real answer is more like 0.000000000000000000000001 to many more decimal places, so it rounds to 0.00.

That is the final answer.

 

[chroot]

Tau:

It is neither 1 nor 0. Please read the earlier posts in the thread.

- Warren