Suppose that (sn) and (tn) are convergent sequences with limsn= sand limtn = t. Then lim (sntn) =st.

Write a proof to this theorem that does not use the theorem that states that "every convergent sequence is bounded." I think that this can be done by using the identitysntn- st =(sn- s)(tn- t) +s(tn- t) +t(sn- s). I am lost from here.