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privetek Group Title

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

  • 2 years ago
  • 2 years ago

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  1. amistre64 Group Title
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    what the limit of lnk as k to inf?

    • 2 years ago
  2. slaaibak Group Title
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    even if the n'th term tends to 0, it doesn't say the series converges.

    • 2 years ago
  3. amistre64 Group Title
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    yeah, was thinking thru the convergence tests :)

    • 2 years ago
  4. slaaibak Group Title
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    harmonic series as an example.

    • 2 years ago
  5. amistre64 Group Title
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    does 1+ln(x) drop faster than x tho?

    • 2 years ago
  6. amistre64 Group Title
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    might need to use a comparison test

    • 2 years ago
  7. privetek Group Title
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    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..

    • 2 years ago
  8. slaaibak Group Title
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    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)

    • 2 years ago
  9. Algebraic! Group Title
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    just use 1/k as a comparison

    • 2 years ago
  10. privetek Group Title
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    would 1/k be less than 1/1+lnk ?

    • 2 years ago
  11. Algebraic! Group Title
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    yes

    • 2 years ago
  12. Algebraic! Group Title
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    that's the point

    • 2 years ago
  13. privetek Group Title
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    great, thanks!! :)

    • 2 years ago
  14. Algebraic! Group Title
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    sure:)

    • 2 years ago
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