# Another problem

how do i find the area of a rectanglewith sides 400root of 400 raised continously to itself like x^x^x^..and 800root of 800 raised also to itself continouslylike y^y^y...
leave answer in whole number not exponent

dextercioby
Homework Helper
What do those "..." mean...?I can assume you'd have to evaluate

$$400^{400^{400^{...}}}\cdot 800^{800^{800^{...}}}$$

Daniel.

HallsofIvy
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Do you have any reason to think that such a sequence converges?

dextercioby
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Read mathworld's page on the power tower.I'm sure u'll find the upper limit for the convergence interval,that is,of course,if u meant the infinite superpower of 400 and 800 respectively.

Daniel.

saltydog
Homework Helper
Abia, consistent no doubt. I think you mean a power tower like:

"The 400'th root of 400"

$$\sqrt[400]{400}\approx 1.01509$$

I think that's in the range of convergence.

Edit: The 800 one too for that matter.

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area of rectangle with lenght x^x^x^x^x.....
and breath y^y^y^y^y^y..... where x is 400^ 1/400 and y is 800^ 1/800.
leaving answer in whole number not decimal or exponent

saltydog
Homework Helper
abia ubong said:
leaving answer in whole number not decimal or exponent
Hello Abia. Yea, leaving it in whole numbers . . . hum . . . how about expressing the power towers in terms of Lambert W-functions (which can be done and in whole numbers), and in this way then the area is just a product of two such expressions.

mathelord
do not understand
pls explain

saltydog