I'll guess the limit is 90 degrees on the grounds that random vectors in high dimensional spaces tend to be orthogonal.
From: asimovd@aol.com
Let v_n be the vector in R^(n-1) defined as (1/n, 2/n,...,(n-1)/n).
Let w_n be the vector in R^(n-1) with the same coordinates in reverse order.
Find the limit as n -> oo of the angle between v_n and w_n.
(Try this without using numerical approximation or summation-of-powers formulae.)
Is there a simple geometric reason for the answer? I don't know.
--Dan
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<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Let v_n be the vector in R^(n-1) defined as (1/n, 2/n,...,(n-1)/n). <BR> <BR> Let w_n be the vector in R^(n-1) with the same coordinates in reverse order.<BR> <BR> Find the limit as n -> oo of the angle between v_n and w_n.<BR> <BR> (Try this without using numerical approximation or summation-of-powers formulae.)<BR> <BR> Is there a simple geometric reason for the answer? I don't know.<BR> <BR> --Dan</FONT></HTML>
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