A First Course in Complex Analysis · Problem 7.5.8

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

Mathematics — Complex Analysis · accumulation-points-sequences

Problem

Let

(a_n)

be a sequence. A point

a

is an accumulation point of the sequence if for every

\epsilon > 0

and every

N \in \mathbb{Z}_{>0}

there exists some

n > N

such that

|a_n - a| < \epsilon

. Prove that if a sequence has more than one accumulation point then the sequence diverges.