Tính giá trị các biểu thức sau: a) A=1−2+3−4+...+97−98+99−100 b) B=1−2−3

* Hướng dẫn giải

a)

$$\begin{gathered} C=1-2+3-4+\mathrm{...}+97-98+99-100 \\ \begin{array}{l}=\left(1-2\right)+\left(3-4\right)+\mathrm{...}+\left(97-98\right)+\left(99-100\right)\\ =-1+\left(-1\right)+\mathrm{...}+\left(-1\right)+\left(-1\right)\\ =-1.50\\ =-50.\end{array} \end{gathered}$$

b)

$$\begin{gathered} B=1-2-3+4+5-6-7+\mathrm{...}+97-98-99+100 \\ \begin{array}{l}=\left(1-2\right)+\left(-3+4\right)+\left(5-6\right)+\mathrm{...}+\left(97-98\right)+\left(-99+100\right)\\ =-1+1+\left(-1\right)+\mathrm{...}+\left(-1\right)+1\\ =\left(-1+1\right)+\left[\left(-1\right)+1\right]+\mathrm{...}+\left[\left(-1\right)+1\right]-1\\ =0+0+\mathrm{...}+0-1\\ =-1.\end{array} \end{gathered}$$