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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
    • 2 years ago
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    what the limit of lnk as k to inf?

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

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

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

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

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

  7. privetek
    • 2 years ago
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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..

  8. slaaibak
    • 2 years ago
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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)

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

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

  11. Algebraic!
    • 2 years ago
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    yes

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

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

  14. Algebraic!
    • 2 years ago
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    sure:)

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