Is not enough for a sequence being monotonic and bounded for $n \geq n_0$?

Question

I am studying Sequences and Series, and doing some exercises I realized that I could use the convergence result for monotonic sequences.

The sequence is bounded, but just monotonic for $n \geq n_0$, where $n_0$ is a fixed positive integer. The theorem still holds ?

Answer 1

Yes, the theorem still hold. The sequence converges towards the superior bound.

Answer 2

Of course. A finite prefix of a sequence never affect its limit.