New user? Sign up

Existing user? Log in

What is \(\displaystyle\lim_{n\rightarrow\infty}\dfrac{A}{B},\) where \(A=n^{(n-1)^{(n-2)^{\ldots^{3^2}}}}\) and \(B=2^{3^{4^{\ldots^{(n-1)^n}}}}\)? I suspect it is \(0,\) but I don't have any idea how I would go about proving this. A little help?

Note by Trevor B. 2 years, 11 months ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

Sort by:

Those terms should be defined as \( A_n\) and \(B_n\).

Hint: How does \( A_n \) and \( A_{n-1} \) relate? What about \( B_n \) and \( B _{n-1} \)?

Which test does that suggest we apply?

Log in to reply

While it is obvious that \(A_n=n^{A_{n-1}},\) I can't come up with a mathematical relartion for \(B_{n-1}\) and \(B_n,\) since \(B_n\neq B_{n-1}^n.\)

I have a question, though. If the B grows faster, than the equation would near zero. If A grows faster, the equation would near infinity... right?

Am I missing something right now?

Wait, I think im pretty close.

The way I look at it, the limit of \(\frac{A}{B}\) would be in the form \(\frac{\inf}{\inf}\),

Certainly, but the question would be which sequence (see Calvin Lin's comment) grows faster.

Oh, ok, thanks

suppose the value of pie =0.31825. calculate the area of circle of radius= 5 equal to 78.55 . please share the answer ok.

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestThose terms should be defined as \( A_n\) and \(B_n\).

Hint:How does \( A_n \) and \( A_{n-1} \) relate? What about \( B_n \) and \( B _{n-1} \)?Which test does that suggest we apply?

Log in to reply

While it is obvious that \(A_n=n^{A_{n-1}},\) I can't come up with a mathematical relartion for \(B_{n-1}\) and \(B_n,\) since \(B_n\neq B_{n-1}^n.\)

Log in to reply

I have a question, though. If the B grows faster, than the equation would near zero. If A grows faster, the equation would near infinity... right?

Am I missing something right now?

Log in to reply

Wait, I think im pretty close.

Log in to reply

The way I look at it, the limit of \(\frac{A}{B}\) would be in the form \(\frac{\inf}{\inf}\),

Log in to reply

Certainly, but the question would be which sequence (see Calvin Lin's comment) grows faster.

Log in to reply

Oh, ok, thanks

Log in to reply

suppose the value of pie =0.31825. calculate the area of circle of radius= 5 equal to 78.55 . please share the answer ok.

Log in to reply