Consider the series
![\[ \sum_{n=1}^{\infty} \frac{(-1)^n}{\log \left( 1 + \frac{1}{n}\right)}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-104b2c90eb6e803818bced2b8522f85b_l3.png "Rendered by QuickLaTeX.com")
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
The given series diverges.
Proof. The series diverges since the limit
![\[ \lim_{n \to \infty} \frac{(-1)^n}{n^{\frac{1}{n}}} \neq 0. \qquad \blacksquare\]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-a3c3e51cc077203b0750b441bab1c589_l3.png "Rendered by QuickLaTeX.com")
Consider the series
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
The given series diverges.
Proof. The series diverges since the limit