Question

Tinh: \(X=\frac{1}{2x3}+\frac{1}{3x4}+....+\frac{1}{9x10}\)

Answer 1

\(X=\frac{1}{x}\cdot\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\right)\)

\(=\frac{1}{x}\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{1}{x}\cdot\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{1}{x}\cdot\frac{2}{5}\)

Answer 2

\(X=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+......+\frac{1}{9x10}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\)

\(=\frac{1}{2}-\frac{1}{10}\)

\(=\frac{5}{10}-\frac{1}{10}=\frac{4}{10}=\frac{2}{5}\)

Answer 3

\(X=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(X=\frac{1}{2}-\frac{1}{10}\)

\(X=\frac{2}{5}\)