Area of rectangle with sides 400^(400^(400^...)) and 800^(800^(800^...))

[abia ubong]

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]

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

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

Daniel.

 

[HallsofIvy]

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

 

[dextercioby]

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]

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.

 

[abia ubong]

area of rectangle with length 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]

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]

do not understand
pls explain

Check out Power Towers, and Lambert W-functions in MathWorld. Try that first.