Mixed state representation in bra-ket form

Question

Hi, am I right, that mixed states can only be stated in words or by a density matrix? Since as soon as I write some thing as

\(\Psi \rangle = \frac{1}{\sqrt{2}}\left(|\psi_1\rangle +|\psi_2\rangle \right) \)

This expresses a pure state. So how do I express a mixed state?

Comments

$\rho=\frac{1}{2}\left(|\psi_1\rangle\langle\psi_1|+|\psi_2\rangle\langle\psi_2|\right)$