Convergence or divergence of a series

If sequence {a_n} is bounded, then {a_n} converges?

Is the statement true or false? please explain why if true or give counter example is false.

False; consider the sequence {(-1)^n} = {-1, 1, -1, 1, ...}, which is bounded but divergent.

I hope this helps!

It's not true. Take sin(n). Then the sequence is bounded by -1 below and 1 above, but it never converges to an actual value.

However, if you add a condition of monotonicity, then it is true.