Why this :$\sum\limits_{n=1}^\infty\frac1{n\sin n}$ is not harmonic series and is convergent?

Question

I'm confused how this series :$$\displaystyle \sum_{n=1}^\infty\frac1{n\sin n}$$ is a convergent series as wolfram show here and it's not harmonic series in the same time .

My question here is:

Why this :$$\displaystyle \sum_{n=1}^\infty\frac1{n\sin n}$$ is not harmonic series and is convergent ?

Answer 1

Hint: According to the answer by @J.R. given at this question the sequence \begin{align*} \left(\frac{1}{n\sin n}\right)_{n\geq 1} \end{align*} is not convergent. We conclude the series \begin{align*} \sum_{n=1}^\infty\frac{1}{n\sin n} \end{align*} is divergent.