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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?

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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?

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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 $B_n\neq B_{n-1}^n.$

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

Wait, I think im pretty close.

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?

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

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$</code> ... <code>$</code>...<code>."> Easy Math Editor

`*italics*`

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italics`**bold**`

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

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Remember to wrap math in $</span> ... <span>$ or $</span> ... <span>$ 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

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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?

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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 $B_n\neq B_{n-1}^n.$

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

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

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Oh, ok, thanks

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Wait, I think im pretty close.

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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

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