{an},{bn} are such that {an } converges to 0.
also, | bn - b | < an .
now, using the definition of convergence of the sequence, to each ε > 0 , there exists m a positive integer such that
| an - 0 | < ε for all n > m.
keeping the definition of convergence in view, consider | b
n- b |
a
n 
| a
n -o| < ε for all n > m.
∴ { bn} converges to b. or { bn} --> b.