Real sequence/Positive/Divergent to infinity and inverse null sequence/Exercise

Let ${\left(x_n\right)}_{n\in \mathbb{N}}$ be a real sequence with $x_n>0$ for all $n\in \mathbb{N}$. Prove that the sequence diverges to $+\mathrm{\infty }$ if and only if the sequence ${\left(\frac{1}{x_n}\right)}_{n\in \mathbb{N}}$ converges to $0$.

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