Convergence of a sequence in $\mathbb R^n$ with a special property Hi folks, I'm trying to prove (or find a counterexample) of this statement:
Let $(x_k)$ be a sequence in $\mathbb R^n$
 such that  $(x_k - x_{k+1})\to0$,
show that $(x_k)$ converge.

$x_n = \sum_{k=1}^n\dfrac1{k}$.
Also,
I think you should use
different letters
for the dimension
($\mathbb R^n$)
and index
($x_n - x_{n+1}$).
