3. Let the general term formula 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
A. $\lambda-3$
D. $\lambda>3$
3. $\mathrm{C}$ Since the sequence $\left\{a_{n}\right\}$ is a monotonically increasing sequence, $a_{n+1}-a_{n}>0\left(n \in \mathbf{N}_{+}\right)$ always holds.

Also, $a_{n}=n^{2}+\lambda n\left(n \in \mathbf{N}_{+}\right)$, so $(n+1)^{2}+\lambda(n+1)-\left(n^{2}+\lambda n\right)>0$ always holds, which means $2 n+1+\lambda>0$. Therefore, $\lambda>$ - $(2 n+1)\left(n \in \mathbf{N}_{+}\right)$ always holds.
Since $n \in \mathbf{N}_{+},-(2 n+1)_{\max }=-3(n=1)$, we have $\lambda>-3$. Hence, the answer is $\mathrm{C}$.