?Show that \(\sum_{n=2}^{\infty} \frac{1}{(\ln n)^{\ln \ln n}}\)diverges. [Hint: Use

Chapter 10, Problem 47

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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 \( x \geq 1\).]

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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:- \(\sum_{n=2}^{\infty} \frac{1}{(\ln n)^{\ln \ln n}}\).

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