tính giới hạn lim[1/1.2 +1/2.3+...+1/n(n+1)]

* Hướng dẫn giải

Đáp án C

Ta có:  

$$\begin{gathered} \frac{1}{1.2}+\frac{1}{2.3}+\dots +\frac{1}{n\left(n+1\right)} \\ =\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3} \\ +\dots +\frac{1}{n}-\frac{1}{n+1}=1-\frac{1}{n+1} \end{gathered}$$

Suy ra:

 $$\begin{gathered} \lim \left[\frac{1}{1.2}+\frac{1}{2.3}+\dots +\frac{1}{n\left(n+1\right)}\right] \\ =\lim \left(1-\frac{1}{n+1}\right)=1. \end{gathered}$$