Question

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

Answer 1

This is the wrong section, buddy.

Answer 2

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

Answer 3

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.