Solution Found!
?Show that \(\sum_{n=2}^{\infty} \frac{1}{(\ln n)^{\ln \ln n}}\)diverges. [Hint: Use
Chapter 10, Problem 47(choose chapter or problem)
QUESTION:
Show that
\(\sum_{n=2}^{\infty} \frac{1}{(\ln n)^{\ln \ln n}}\)
diverges. [Hint: Use Formula 1.5.10 \(\left(x^{r}=e^{r \ln x}\right)\) and the fact that \(\ln x<\sqrt{x}\) for \( x \geq 1\).]
Questions & Answers
QUESTION:
Show that
\(\sum_{n=2}^{\infty} \frac{1}{(\ln n)^{\ln \ln n}}\)
diverges. [Hint: Use Formula 1.5.10 \(\left(x^{r}=e^{r \ln x}\right)\) and the fact that \(\ln x<\sqrt{x}\) for \( x \geq 1\).]
ANSWER:Step 1 of 6
Given:- \(\sum_{n=2}^{\infty} \frac{1}{(\ln n)^{\ln \ln n}}\).