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 Discussion Response Post to:
lim n
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![[Post New]](/templates/default/images/icon_minipost_new.gif) 8 Sep 2007 03:08:18 IST
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Nice question based on basic concepts of limit...
the given term can be written as..
[nk+1 / (1+1/n)] cos n!
cos n! is always between -1 and 1, and never equal to 1, -1 or 0
(as cos is -1,1 or 0 only at multiples of pi/2, and n! can never be multiple of pi/2 as n! is rational &pi is irrational)
also, cosn! keeps on changing sign as n tends to infinity.
So, for cosn![nk-1 / (1+1/n)],
if k =0, limit tends to 0 as n tends to infinity
if k-1 < 0 ie k < 1
limit tends to zero as n tends to infinity
if k-1 > 0 ie k > 1
limit oscillates between minus infinity to infinity... and so limit does not exist.
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Sudeep Kumar
(B tech, IITd)
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this reply: 7 points
(with 1 
in 2 votes ) [?]
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