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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?
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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across
 2 years ago
Best ResponseYou've already chosen the best response.0This is the wrong section, buddy.

johnsonshelby
 2 years ago
Best ResponseYou've already chosen the best response.0Well, there is no calculus 2 subtopic haha \[\sum_{n=1}^{\infty} \frac{ 1 }{ \ln n ^{\ln n} }\] Is this the equation?

across
 2 years ago
Best ResponseYou've already chosen the best response.0Let \(N=2\), 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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