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 !
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