Is $1/5+1/7+1/11+1/13+1/17+1/19+\cdots$ convergent?
You asked for a hint, so here it is: $$\frac{1}{6k \pm 1} \ge \frac{1}{7k}$$ for all positive integers $k$.
You asked for a hint, so here it is: $$\frac{1}{6k \pm 1} \ge \frac{1}{7k}$$ for all positive integers $k$.