convegence: Xn bounded, lim n->infty (Xn+1-Xn)=0. Prove that

[transgalactic]

i am given a bounded sequence Xn
which follows lim(Xn+1 - Xn)=0
as n->+infinity

k=lim inf Xn
L=lim sup Xn
prove that every number from [k,L]
is a partial bound of Xn

??