Real sequence/Convergence/Unit fractions/Exercise

Let ${\left(x_n\right)}_{n\in \mathbb{N}}$ be a real sequence. Prove that the sequence converges to $x$ if and only if for all $k\in {\mathbb{N}}_{+}$ a natural number $n_0\in \mathbb{N}$ exists, such that for all $n\ge n_0$ the estimation $|x_n-x|\le \frac{1}{k}$ holds.

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