\(\frac{1}{6}\cdot\frac{1}{66}\cdot\frac{1}{176}\)
\(=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}\)
\(=\frac{1}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}\right)\)
\(=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\right)\)
\(=\frac{1}{5}\left(1-\frac{1}{16}\right)\)
\(=\frac{1}{5}\cdot\frac{15}{16}\)
\(=\frac{3}{16}\)
=))
\(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}\)
\(=\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}\)
\(=\frac{1}{5}\times\left(\frac{5}{1\times6}+\frac{5}{6\times11}+\frac{5}{11\times16}\right)\)
\(=\frac{1}{5}\times\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\right)\)
\(=\frac{1}{5}\times\left(1-\frac{1}{16}\right)\)
\(=\frac{1}{5}\times\frac{15}{16}\)
\(=\frac{3}{16}\)
1/6 + 1/66 + 1/75
= 1/1*6 + 1/6*11 + 1/11*16
= 1/5(1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16)
= 1/5(1 - 1/16)
= 1/5*15/16
= 3/16
\(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}\)
=\(\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}\)
\(=\frac{1}{5}\left(\frac{5}{1\times6}+\frac{5}{6\times11}+\frac{5}{11\times16}\right)\)
\(=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\right)\)
\(=\frac{1}{5}\times\frac{15}{16}=\frac{3}{16}\)
