## Calculus (3rd Edition)

$b_m$ converges to $0$.
We have $$\lim _{m \rightarrow \infty} b_m=\lim _{m \rightarrow \infty} \frac{1+(-1)^m}{m}\\ =\lim _{m \rightarrow \infty} \frac{(1/m)+((-1)^m/m)}{1}=0$$ So, $b_m$ converges to $0$.