Re: [math-fun] Limit question

On Fri, 29 Aug 2008, Dan Asimov wrote:

The expression

f(n) = sqrt(1 + sqrt(2 + . . . + sqrt(n)...))

approaches about 1.7579 . Rather quickly, too: For n >= 20, the first 16 digits after the decimal point remain the same.

Is there a closed form for lim n->oo f(n) ?

http://mathworld.wolfram.com/NestedRadicalConstant.html http://www.research.att.com/~njas/sequences/A072449 "No closed-form expression is known for this constant." -Eric