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 [...].