Question

\(\frac{2}{0,11\times0,12}+\frac{2}{0,12\times0,13}+\frac{2}{0,13\times0,14}+....+\frac{2}{0,21\times0,22}=\)

Answer 1

\(\frac{2}{0,11.0,12}+\frac{2}{0,12.0,13}+...+\frac{2}{0,21.0,22}\)

\(=200.\left(\frac{0,01}{0,11.0,12}+\frac{0,01}{0,12.0,13}+...+\frac{0,01}{0,21.0,22}\right)\)

\(=200.\left(\frac{1}{0,11}-\frac{1}{0,12}+\frac{1}{0,12}-\frac{1}{0,13}+...+\frac{1}{0,21}-\frac{1}{0,22}\right)\)

\(=200.\left(\frac{1}{0,11}-\frac{1}{0,22}\right)\)

\(=200.\frac{50}{11}\)

\(=\frac{10000}{11}\)