It looks like the series you're asking about is not formatted correctly. From the given text, it seems you want to check the convergence of a series, but I can't fully decipher the details due to the mixed characters and symbols.

If you can clarify the series or correct any formatting issues, I will be able to analyze it for convergence. It seems you might be asking about:

1. $\sum \tan \left( \frac{1}{n} \right)$ (or some related expression)

Could you please confirm or clarify the series you're referring to? Once clarified, I can check its convergence using appropriate convergence tests like the Ratio Test, Root Test, or Comparison Test.

Let me know if you'd like further assistance!