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February 19th, 2007, 05:20 PM   #1
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the series for convergence test

# sum # log(n.(sin1/n)) is this series convergent or divergent and how???
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February 19th, 2007, 06:52 PM   #2
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Are you asking whether:

∑(n=1, n=∞) log(n*sin(1/n))

converges or diverges?
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February 20th, 2007, 01:28 AM   #3
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yes i couldn't write it like that.That's it
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February 20th, 2007, 09:01 PM   #4
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It converges.
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February 23rd, 2007, 01:23 PM   #5
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i know that it is convergent.I want just a solution
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February 24th, 2007, 03:15 PM   #6
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Approximate each term as a fixed multiple of a power of n.
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May 25th, 2007, 10:08 PM   #7
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it converges

∑(n=1, n=∞) log(n*sin(1/n)) converges

let me show u

lim
an=n___∞ log(n*sin(1/n))

using l'hopital rule

lim
an=n___∞ log((sin(1/n)/(1/n)))


lim lim
an=n___∞ log((1))=0here as a(n+1)<an and n___0 an=0
it converges
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May 26th, 2007, 12:02 AM   #8
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log(n*sin(1/n)) is equivalent to log(n*(1/n-1/(6n^3)+o(n^4)))=log(1-1/(6n^2)+o(n^3))~-1/6n^2 which is the general term of a convergent series.
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