Determine whether or not the sequence with the given nth term is monotonic, then discuss its boundedness (i) an=cosn/n ?

1 Answer
Apr 18, 2018

First of all AA,nin N , -1 <= cos n<=1

Hence , -1/n <= cosn /n <=1/n. Since cos n is a periodic function,
the given sequence {a_n} decreases and then increases in equal intervals monotonically..

Now as n -> oo, -1/n and 1/n ->0
Therefore according to squeeze theorem, the sequence cos n /n is convergent and converges to 0.

Since the sequence is convergent, it is bounded. That means it would have a lower bound and a upper bound.