Question

[phạm văn quyết tâm]

tìm x

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}\)

Answer 1

[Phạm Tuấn Đạt]

\(\frac{1}{21}+\frac{1}{28}+...+\frac{2}{x\left(x+1\right)}\)

\(=\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+1\right)}\)

\(=2\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}\right)\)

\(=2\left(\frac{1}{6}-\frac{1}{x+1}\right)\)

\(=2\left(\frac{x-5}{6x+6}\right)=\frac{2\left(x+5\right)}{2\left(3x+3\right)}=\frac{x+5}{3x+3}\)