Let $G$ be a graph on $n$ vertices and $λ_1\geq λ_2\geq \ldots \geq λ_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{λ_i}.$ In this work, we using an increasing sequence converging to the $λ_1$ to obtain an increasing sequence of lower bounds for $EE(G)$. In addition, we generalize this succession for the Estrada index of an arbitrary nonnegative Hermitian matrix.