Tính: 1/x(x+1) + 1/(x+1)(x+2) + 1(x+2)(x+3) + 1/(x+3)(x+4)

* Hướng dẫn giải

$\begin{array}{l}\frac{1}{\mathrm{x}\left(\mathrm{x}+1\right)}+\frac{1}{\left(\mathrm{x}+1\right)\left(\mathrm{x}+2\right)}+\mathrm{.....}+\frac{1}{\left(\mathrm{x}+4\right)\left(\mathrm{x}+5\right)}-\frac{1}{\mathrm{x}+5}\\ =\frac{1}{\mathrm{x}}-\frac{1}{\mathrm{x}+1}+\mathrm{......}+\frac{1}{\mathrm{x}+4}-\frac{1}{\mathrm{x}+5}+\frac{1}{\mathrm{x}+5}=\frac{1}{\mathrm{x}}\end{array}$