Question

0<=b_n<=a_n.
a) if a_n-->0 then b_n-->0.
b) if a_n-->infinity then b_n-->infinity

I don't know where to start.

Answer 1

well clearly, since b_n is between 0 and a_n, as a_n->0, so does b_n.

Not sure (b) follows. There must be some other conditions on the sequences.