Let $X_t = \theta_1\epsilon_{t-1} + ... + \theta_q\epsilon_{t-q} + \epsilon_t$ where $\epsilon_t$ is a white noise with zero mean variance $\sigma^2$.
$X_t$ is said to be invertible if $\epsilon_t = \sum_{j=0}^\infty \pi_j X_{t-j}$ where $\sum_{j=0}^\infty | \pi_{j}| < \infty$
I want to show \begin{equation} \sigma^2 + E\left(\sum_{j > m} \pi_j X_{m+1-j}\right)^2 \leq \sigma^2 + \left(\sum_{j>m}|\pi_j|\right)^2\gamma(0) \end{equation} where $\gamma(0) = E(X_{t}^2)$ for all $t$.
Also,
\begin{equation} \left(\sum_{j>m}|\pi_j|\right)^2\gamma(0) \leq Kc^m \end{equation} where $K > 0$ and $c \in (0, 1)$
Any hints will be appreciated.