$(n+1)x_{n+2}-nx_{n+1}-x_n=0$ ,prove the sequence converges Sequence $x_n$ for which
$$(n+1)x_{n+2}= nx_{n+1}+x_n$$
for every $n\in\mathbb{N}$. Prove that it converges.
Its not decreasing or increasing, i checked with some random initial values.So, i dont know how to proceed with this. Any help?

Note that $$(x_{n+2}-x_{n+1})=\frac {(x_n-x_{n+1})}{n+1}$$ which should be enough to get you to an answer - the absolute difference between terms reduces very quickly.
