Question

1/5+-1/6+1/7+-1/8+1/9+1/8+-1/7+1/6+-1/5

Answer 1

Ta có:

\(\frac{1}{5}+\frac{-1}{6}+\frac{1}{7}+\frac{-1}{8}+\frac{1}{9}+\frac{1}{8}+\frac{-1}{7}+\frac{1}{6}+\frac{-1}{5}\)

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

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

=\(\frac{0}{5}+\frac{0}{6}+\frac{0}{7}+\frac{0}{8}+\frac{1}{9}\)

=\(\frac{1}{9}\)