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Math and science::Analysis::Tao::06. Limits of sequences

Squeeze test

Let \( (a_n)_{n=m}^{\infty} \), \( (b_n)_{n=m}^{\infty} \) and \( (c_n)_{n=m}^{\infty} \) be sequences of real numbers such that:
\[ a_n \le b_n \le c_n \]
for all \( n \ge m \). Suppose that \( (a_n)_{n=m}^{\infty} \) and \( (c_n)_{n=m}^{\infty} \) both converge to the same limit \( L \). Then [...].