Conditional Convergence

Definition

• Let $\sum a_n$ be a Series
• $\sum a_n$ conditionally converges $⟺\sum |a_n|$ diverges, but $\sum a_n$ converges Or, in other words, our series Converges but does not Absolute Converge

Properties

Rearrangement Property

• If $\sum a_n$ conditionally converges
• Then, $\forall r\in \mathbb{R}$ there exists an arrangement of $\sum a_n$ s.t $\sum a_n=r$