$\large \lim\left(\dfrac{1}{5.9}+\dfrac{1}{9.13}+...+\dfrac{1}{(4n+1)(

$\large \lim\left(\dfrac{1}{5.9}+\dfrac{1}{9.13}+...+\dfrac{1}{(4n+1)(4n+5)} \right )$ bằng

• A. $\large \dfrac{1}{4}$
• B. $\large \dfrac{1}{5}$
• C. $\large \dfrac{1}{36}$
• D. $\large \dfrac{1}{20}$

Chọn D

$\large \lim\left(\dfrac{1}{5.9}+\dfrac{1}{9.13}+...+\dfrac{1}{(4n+1)(4n+5)} \right )$

$\large =\dfrac{1}{4}. \left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{4n+1}-\dfrac{1}{4n+5} \right )$

$\large =\lim\dfrac{1}{4}\left(\dfrac{1}{5}-\dfrac{1}{4n+5} \right )=\dfrac{1}{20}$