If a real sequence converges,then it is bounded.
How can we prove this statement?
Let its limit be L. The very definition of convergence implies the existence of a natural number N such that for every . The former inequality implies in turn that for every
Hence, starting from the N-th element of the sequence you can place them all inside of a disk of radius 1+|L| (and centered at the origin). it's clear that up to this moment some elements of the sequence might remain outside of this disk, but since it's only a finite number of them, we are done, right?