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![[Post New]](/templates/default/images/icon_minipost_new.gif) 3 Apr 2008 00:24:11 IST
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Q1. n   (n!)1/n / n Answer is = 1/e
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3 Apr 2008 00:59:09 IST
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rewrite the ques as
y = (n ! /n n) 1/n
log y = 1/n log (n!/n n )
=0  1 log (1-x) dx
= -1
hence y = e-1 = 1/e
rate me
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3 Apr 2008 17:37:38 IST
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Perfect answer arpan. Superb.
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Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi |
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3 Apr 2008 19:16:45 IST
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thank u 
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3 Apr 2008 20:29:18 IST
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well done buddy
main part is
logA = (1/n) [n ] [ ] log[( n(n-1)(n-2)(n-3)(n-4)................3.2.1)/nn] (opening n!)
now we can write n.n.n.n.n.............n times = nn
so the =n becomes
logA = (1/n) [n ][ ] log[(n/n)((n-1)/n)((n-2)/n).............(3/n).(2/n).(1/n)]
= [n ][ ] (1/n) summation (r = 0 to n-1) (n - r/n)
= [o ][1 ] 1 . log (1-x)dx
solve it as stated above :)
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