Absolute convergence criterion
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Absolute convergence criterion
Let \( \displaystyle \left( y_{n} \right)_{n\in \mathbb{N}} \) be a sequence of real numbers such that : for all sequences \( \displaystyle \left( x_{n} \right)_{n\in \mathbb{N}} \) of real numbers with \( \displaystyle \lim_{n}x_{n} = 0 \) the series \( \displaystyle \sum_{n=1}^{\infty} x_{n}y_{n} \) converges. Then \( \displaystyle \sum_{n=1}^{\infty} | y_{n} | < + \infty \).
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