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y?

  • 2 years ago

sum from n=2 to infinity of 1/((ln(n))^(ln(n))) does it converge or diverge?

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  1. across
    • 2 years ago
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    This is the wrong section, buddy.

  2. johnsonshelby
    • 2 years ago
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    Well, there is no calculus 2 subtopic haha \[\sum_{n=1}^{\infty} \frac{ 1 }{ \ln n ^{\ln n} }\] Is this the equation?

  3. across
    • 2 years ago
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    Let \(N=2\), and\[f(n)=\frac{1}{\ln n^{\ln n}}.\]Then, since \(f\) is monotonically decreasing on \([N,\infty)\), you can use the integral test for convergence:\[\int_{N}^{\infty}f(n)\,dn=\int_{2}^{\infty}\frac{1}{\ln n^{\ln n}}\,dn=\infty.\]Therefore, the series diverges.

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