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## privetek 2 years ago determine whether the series converges: sum(k=1 -> infinity) [1/(1+lnk)]

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1. amistre64

what the limit of lnk as k to inf?

2. slaaibak

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

3. amistre64

yeah, was thinking thru the convergence tests :)

4. slaaibak

harmonic series as an example.

5. amistre64

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

6. amistre64

might need to use a comparison test

7. privetek

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..

8. 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)

9. Algebraic!

just use 1/k as a comparison

10. privetek

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

11. Algebraic!

yes

12. Algebraic!

that's the point

13. privetek

great, thanks!! :)

14. Algebraic!

sure:)

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