Thu gọn ​\(\begin{aligned} &\text { } \frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+\ldots+\frac{5}{(4 n-1)(4 n+3)} \end{aligned}\) ta được

* Hướng dẫn giải

 \(\begin{aligned} &\text { B= } \frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+\ldots+\frac{5}{(4 n-1)(4 n+3)}\\ &=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\cdots+\frac{1}{4 n-1}-\frac{1}{4 n+3}\right)\\ &=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{4 n+3}\right)=\frac{5}{4} \cdot \frac{4 n}{3(4 n+3)}=\frac{5 n}{3(4 n+3)} \end{aligned}\)