\(\lim \left[ {\dfrac{1}{{1.2}} + \dfrac{1}{{2.3}} + ... + \dfrac{1}{{n\left( {n + 1} \right)}}} \right]\) bằng:

* Hướng dẫn giải

Ta có:

\(\begin{array}{l}\dfrac{1}{{1.2}} + \dfrac{1}{{2.3}} + ... + \dfrac{1}{{n\left( {n + 1} \right)}} = \dfrac{1}{1} - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + ... + \dfrac{1}{n} - \dfrac{1}{{n + 1}} = 1 - \dfrac{1}{{n + 1}}\\ \Rightarrow \lim \left[ {\dfrac{1}{{1.2}} + \dfrac{1}{{2.3}} + ... + \dfrac{1}{{n\left( {n + 1} \right)}}} \right] = \lim \left( {1 - \dfrac{1}{{n + 1}}} \right) = 1\end{array}\)

Chọn B.