Question

determine whether the series converges:
sum(k=1 -> infinity) [1/(1+lnk)]

Answer 1

what the limit of lnk as k to inf?

Answer 2

even if the n'th term tends to 0, it doesn't say the series converges.

Answer 3

yeah, was thinking thru the convergence tests :)

Answer 4

harmonic series as an example.

Answer 5

does 1+ln(x) drop faster than x tho?

Answer 6

might need to use a comparison test

Answer 7

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..

Answer 8

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)

Answer 9

just use 1/k as a comparison

Answer 10

would 1/k be less than 1/1+lnk ?

Answer 11

yes

Answer 12

that's the point

Answer 13

great, thanks!! :)

Answer 14

sure:)