anonymous
  • anonymous
determine whether the series converges: sum(k=1 -> infinity) [1/(1+lnk)]
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
what the limit of lnk as k to inf?
slaaibak
  • slaaibak
even if the n'th term tends to 0, it doesn't say the series converges.
amistre64
  • amistre64
yeah, was thinking thru the convergence tests :)

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slaaibak
  • slaaibak
harmonic series as an example.
amistre64
  • amistre64
does 1+ln(x) drop faster than x tho?
amistre64
  • amistre64
might need to use a comparison test
anonymous
  • anonymous
yes, that's what i was thinking.. i got -- 1/(1+lnk) > 1/lnk and i don't know where to go from here or this is even right..
slaaibak
  • slaaibak
it's the other way around. 1/lnk > 1/(1+ lnk) so if you can determine whether 1/ln k converges, you can say /1(1+lnk) converges. but if 1/lnk diverges, you can't say anything about 1/(1+lnk)
anonymous
  • anonymous
just use 1/k as a comparison
anonymous
  • anonymous
would 1/k be less than 1/1+lnk ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
that's the point
anonymous
  • anonymous
great, thanks!! :)
anonymous
  • anonymous
sure:)

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