Take the 2-minute tour ×  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.
share|improve this question @Mohamad: You're mixing up sequences
and 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. –  Zev
Chonoles Jun 24 '12 at 19:30 See this question –  Julián Aguirre
Jun 24 '12 at 21:13  3 Answers 3  Have you tried using squeeze
theorem here. It is quite useful in calculating limits of
functions. See it might work for series as well because you are
using the concept of convergence of the series of partial sum of
$A_n$ and $C_n$.  share|improve this answer  To prove this, the
hypothesis must be strengthened very slightly. We will assume
not only that the partial sums are bounded, but also that the
partial sums of $A_n$ and