Does it diverge or converge?

Calculus Level 3

Does the following series diverge or converge?

$\sum _{n=1}^{\infty } \dfrac{\sin(\text{ln}(n))}{n}.$

The Basics:
Let $$\sum_{n=m}^\infty a_n$$ be a formal infinite series. For any integer $$N\geqslant m$$, we define the $$N^{\text{th}}$$ partial sum $$S_N$$ of this series to be $$S_N:=\sum_{n=m}^N a_n$$; of course, $$S_N$$ is a real number. If the sequence $$(S_N)_{n=m}^\infty$$ converges to some limit $$L$$ as $$N\to\infty$$, then we say that the infinite series $$\sum_{n=m}^\infty a_n$$ is convergent, and converges to $$L$$; we also write $$L=\sum_{n=m}^\infty a_n$$, and say that $$L$$ is the sum of the infinite series $$\sum_{n=m}^\infty a_n$$. If the partial sums $$S_N$$ diverge, then we say that the infinite series $$\sum_{n=m}^\infty a_n$$ is divergent.

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