Tính 

- Hướng dẫn giải

$$\begin{gathered} A=-1^2+2^2-3^2+4^2-\mathrm{...}-{99}^2+{100}^2 \\ \begin{array}{l}=\left(2^2-1^2\right)+\left(4^2-3^2\right)+\mathrm{...}+\left({100}^2-{99}^2\right)\\ =1+2+3+4+\mathrm{...}+99+100\\ =\frac{\mathrm{100...101}}{2}=5050\end{array} \end{gathered}$$