## y? Group Title sum from n=2 to infinity of 1/((ln(n))^(ln(n))) does it converge or diverge? one year ago one year ago

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1. across Group Title

This is the wrong section, buddy.

2. johnsonshelby Group Title

Well, there is no calculus 2 subtopic haha $\sum_{n=1}^{\infty} \frac{ 1 }{ \ln n ^{\ln n} }$ Is this the equation?

3. across Group Title

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.