Compare with $b_n = \frac{1}{n}$; limit is $\frac{2}{\pi}$; series diverges

Compare with $b_n = \frac{1}{n^2}$; limit is $\frac{2}{\pi}$; series converges

Compare with $b_n = \frac{1}{n}$; limit is $0$; series converges

Compare with $b_n = \frac{1}{n^2}$; limit is $0$; test is inconclusive