Are the following statements true or false? If the statement is false, justify your answer. (2 points each) 1. Let {an} and {b, } be sequences such that an _ by for all n, lim an = a, and n-+00 lim by = b. Then a > b. n-+00 2. Suppose {an } and {b, } are sequences with lim an = a and lim (an - by) = 0. Then, n-+co n-+00 lim bn = a. n-+0o 4. If both Can and on are divergent then an infinite series of the form (an - br) n=1 n=1 n=1 is always divergent.

pur-new-sol