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Compute \(\sqrt{11 \sqrt{11 \sqrt{11 {\sqrt \dotsb}}}}\)

 Jul 18, 2020
 #1
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I made a mistake in my calculations....as guest found below... answer is 11 .       yikes.

 

Let x =   sqrt 11(sqrt11 (sqrt11......     your question

x2 = 11 sqrt 11 sqrt 11......        this is   11x

so 

x2 = 11x    divide by x

x = 11             Well ...that was easy!   D'Oh!   

 

Thanx, Guest !

 Jul 18, 2020
edited by ElectricPavlov  Jul 18, 2020
edited by ElectricPavlov  Jul 18, 2020
 #2
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EP: Remember the exponent is the reciprocal of the sum of powers of 2 to infinity:1/2+1/4+1/8+1/16.......to infinity =1. Or 11^1 =11.
You can easily see it in this very short computer code evaluated to 250 terms, which gives:
c=1; listfor(n, 1, 250, listforeach(b,reverse (d=11), c=2#(b * c);print c
10.9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9999999999 9998542112 6061640964 38049071

 Jul 18, 2020

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