Câu hỏi của một bạn:
lim(2nn+1)(n+3)(n+1)(n+2)=limnn(2+1nn)n(1+3n)n2(1+1n)(1+2n)=lim(2+1nn)(1+3n)(1+1n)(1+2n)=2\begin{array}{ll}&\lim\dfrac{(2n\sqrt{n}+1)(\sqrt{n}+3)}{(n+1)(n+2)}\\ =&\lim\dfrac{n\sqrt{n}\left(2+\dfrac{1}{n\sqrt{n}}\right)\sqrt{n}\left(1+\dfrac{3}{\sqrt{n}}\right)}{n^2\left(1+\dfrac{1}{n}\right)\left(1+\dfrac{2}{n}\right)}\\ =&\lim\dfrac{\left(2+\dfrac{1}{n\sqrt{n}}\right)\left(1+\dfrac{3}{\sqrt{n}}\right)}{\left(1+\dfrac{1}{n}\right)\left(1+\dfrac{2}{n}\right)}\\=&2\end{array}===lim(n+1)(n+2)(2nn+1)(n+3)limn2(1+n1)(1+n2)nn(2+nn1)n(1+n3)lim(1+n1)(1+n2)(2+nn1)(1+n3)2