A First Course in Complex Analysis · Problem 7.5.14

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · squeeze-theorem

Problem

Prove that, if

a_n \leq b_n \leq c_n

for all

n

and

\lim_{n\to\infty} a_n = \lim_{n\to\infty} c_n = L

, then

\lim_{n\to\infty} b_n = L

. This is called the Squeeze Theorem, and is useful in testing a sequence for convergence.