8. Let the general term of the sequence $\left\{a_{n}\right\}$ be $a_{n}=n^{2}+\lambda n\left(n \in \mathbf{N}_{+}\right)$, if $\left\{a_{n}\right\}$ is a monotonically increasing sequence, then the range of the real number $\lambda$ is $\qquad$.
\begin{array}{l}\text { 8. } \lambda>-3 \text {. } \\ a_{n+1}-a_{n}=(n+1)^{2}+\lambda(n+1)-n^{2}-\lambda n=2 n+1+\lambda>0 \text {, so } \lambda>-(2 n+1)(n \in \\ \mathbf{N}_{+})(2 n+1)_{\max }=-3 \text {. Therefore, } \lambda>-3 .\end{array}