Abel’s_Test

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Definition

Let $(b_n)$ be a sequence satisfying $b_1 \geq b_2 \geq b_3 \geq \cdots \geq 0$ with $\lim b_n = 0$. If the series $\sum_{n=1}^{\infty} a_n$ has bounded partial sums, then the series $\sum_{n=1}^{\infty} a_n b_n$ converges.