[math-fun] Limit question
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) ? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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
The constant : 1.75793275661800453270881963821813852765319992214683770431013550038511023267444675757234455400025945297093 does not fit anything I have, I made all the tests I know up to 100 digits with it. Simon Plouffe
participants (3)
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Dan Asimov -
Eric W. Weisstein -
Simon Plouffe