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Math Help - converge or diverge?

  1. #1
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    converge or diverge?

    infinity
    summation of ln(n)/n
    n=2

    I need to know if it converges or diverges and explain why. If someone could go though this step by step it would be a big help.
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  2. #2
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    Quote Originally Posted by thatloserrsaid View Post
    infinity
    summation of ln(n)/n
    n=2

    I need to know if it converges or diverges and explain why. If someone could go though this step by step it would be a big help.
    use the integral test
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    the integral test confuses me.. thats why i requested a step by step help
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  4. #4
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    Quote Originally Posted by skeeter View Post
    use the integral test
    the integral test confuses me.. thats why i requested a step by step help
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  5. #5
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    Quote Originally Posted by thatloserrsaid View Post
    the integral test confuses me.. thats why i requested a step by step help
    \int_2^{\infty} \frac{\ln{x}}{x} \, dx

    substitution ... let u = \ln{x}

    give it a go.
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  6. #6
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    Quote Originally Posted by skeeter View Post
    \int_2^{\infty} \frac{\ln{x}}{x} \, dx

    substitution ... let u = \ln{x}

    give it a go.


    after i integrate i get [ln(x)]^2 / 2
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  7. #7
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    Quote Originally Posted by thatloserrsaid View Post
    infinity
    summation of ln(n)/n
    n=2

    I need to know if it converges or diverges and explain why. If someone could go though this step by step it would be a big help.
    \frac{ln(n)}{n}\geq\frac{1}{n} for n\geq e
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  8. #8
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    D'Alembert's test

    please see attachment:
    Attached Files Attached Files
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