Ta có : $16A=\dfrac{16}{6.10}+\dfrac{16}{7.9}+\dfrac{16}{8.8}+\dfrac{16}{9.7}+\dfrac{16}{10.6}$
$=>16A=\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{7}+\dfrac{1}{9}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{7}+\dfrac{1}{10}+\dfrac{1}{6}$
$=>16A=2.(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})$
$=>A=\dfrac{1}{8}(dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10})$
\(A=\dfrac{1}{6.10}+\dfrac{1}{7.9}+\dfrac{1}{8.8}+\dfrac{1}{9.7}+\dfrac{1}{10.6}\)
\(16A=\dfrac{16}{6.10}+\dfrac{16}{7.9}+\dfrac{16}{8.8}+\dfrac{16}{9.7}+\dfrac{16}{10.6}\)
\(16A=\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{7}+\dfrac{1}{9}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{7}+\dfrac{1}{10}+\dfrac{1}{6}\)
\(16A=2\left(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}\right)\)
\(A=2:16\left(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}\right)\)
\(A=\dfrac{1}{8}\left(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{10}\right)\left(đpcm\right)\)
