Given three series $A_n \leq B_n \leq C_n$, I should prove that $B_n$ is convergent if the series of the partial sums of $A_n$ and $C_n$ are convergent.
How to prove that a series is convergent
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calculus
sequences-and-series
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1@Mohamad: You're mixing up [sequences and series](http://en.wikipedia.org/wiki/Sequence#Series). Usually one is interested in the **sequence** of partial sums of a sequence, or the **series associated to** a sequence (the series whose terms are precisely that sequence); and $A_n$, $B_n$, and $C_n$ are themselves sequences, not series. – 2012-06-24
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0See [this question](http://math.stackexchange.com/questions/157853/proof-of-a-test-for-series/157862#157862) – 2012-06-24