Giới hạn lim[(2-5n)^3(n+1)^2/2-25n^5] bằng? A.-4 B.-1 C.5 D.-3/2

* Hướng dẫn giải

$\lim \frac{{(2-5n)}^3{(n+1)}^2}{2-25n^5}=\lim \frac{\frac{{(2-5n)}^3}{n^3}.\frac{{(n+1)}^2}{n^2}}{\frac{2-25n^5}{n^5}}=\frac{{\left(\frac{2-5n}{n}\right)}^3.{\left(\frac{n+1}{n}\right)}^2}{\frac{2}{n^5}-25}$

$=\lim \frac{{\left(\frac{2}{n}-5\right)}^3.{\left(1+\frac{1}{n}\right)}^2}{\frac{2}{n^5}-25}=\frac{{\left(0-5\right)}^3{\left(1+0\right)}^2}{0-25}=\frac{{(-5)}^3{.1}^2}{-25}=5$