Does $1+\frac{1}{3}-\frac{2}{5}+\frac{1}{7}+\frac{1}{9}-\frac{2}{11}+...$ converge?

Question

I'm having a hard time figuring if the following series converges or diverges. $$ 1+\frac{1}{3}-\frac{2}{5}+\frac{1}{7}+\frac{1}{9}-\frac{2}{11}\:+\:... $$

I think that if I'll place the brackets in the right place I can figure what type of series are laying under. But I can't figure it out. Any help is appreciated!

Answer 1

Hint: each group of three terms is of the form $$\frac{1}{3k-2}+\frac{1}{3k}-\frac{2}{3k+2}=\frac{18k-4}{27k^3-12k}.$$