Let $(U_n)$ be a sequence such as $|u_{n+1}-u_n|<\frac{1}{n^2}$ show that (U_n) is a convergent sequence.
I m stuck with this question, I showed that $\lim\limits_{n \to \inf} u_{n+1}-u_n =0$ Can you help me ?
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2Possible duplicate of To show that ${x_n}$ is convergent where $|x_{n+1} - x_n|< \frac{1}{n^2}$ – Martin R Jul 13 '19 at 18:11
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it's cauchy cause $|u_m-u_n| < \sum_{j=n}^m \frac{1}{j^2}$ goes to $0$ as $m,n \to \infty$. – mathworker21 Jul 13 '19 at 18:11