calculus - Nature of infinite series

I was doing some exercises on the nature of infinite series when I came across this one intriguing series - $$\sum_{i=1}^{\infty}\frac{(-1)^{i-1}}{\ln(i+1)}.$$ I tried to solve it with D'Alembert's ratio test and came at the solution that this series is convergent as $\lim\limits_{n \to \infty}|\frac{u_{n+1}}{u_n}|$ comes out to be $\lim\limits_{n \to \infty}|\frac{-\ln(n+1)}{\ln(n+2)}| = \lim\limits_{n \to \infty}\frac{\ln(n+1)}{\ln(n+2)}$ which is smaller than 1 as $\ln x$ is strictly increasing. So, the $-$ sign doesn't really make any difference. But the answer in the textbook is that this series is conditionally convergent, meaning that it wouldn't have been convergent if not for the $-$ sign. Can anyone explain this to me?