Kết quả của phép tính: 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 +....+99 - 100

Bài 1:

\(S=\frac{27.4500+135.550.2}{2+4+6+...+18}\)

\(S=\frac{270.450+270.550}{\left(2+18\right)+\left(4+16\right)+\left(6+14\right)+\left(8+12\right)+10}\)

\(S=\frac{270.\left(450+550\right)}{20+20+20+20+10}\)

\(S=\frac{270.1000}{90}=3000\)

Bài 7:

\(A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)

\(=\frac{-1}{4.5}+\frac{-1}{5.6}+\frac{-1}{6.7}+\frac{-1}{7.8}+\frac{-1}{8.9}+\frac{-1}{9.10}\)

\(=\left(\frac{1}{5}-\frac{1}{4}+\frac{1}{6}-\frac{1}{5}+\frac{1}{7}-\frac{1}{6}+\frac{1}{8}-\frac{1}{7}+\frac{1}{9}-\frac{1}{8}+\frac{1}{10}-\frac{1}{9}\right)\)

\(=\frac{1}{10}-\frac{1}{4}=\frac{-3}{20}\)