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We have that $(x_n)$ is a sequence of real numbers. And the relation on the title: $$ |x_{n+1} - x_n| < \frac{1}{3^n}. $$ We must prove that this is a Cauchy sequence.

I know that an Cauchy sequence follows the definition:

given $\epsilon>0$, exists $n_0 > 0$, such that $m,n > n_o \Rightarrow |x_m - x_n|< \epsilon$

But I don't know how to use both informations to prove the exercise.

If someone please may help me, I'd be very thankful.