Задача №2101

\[ \lim_{n\to\infty}\frac{(n+1)^3+(n+2)^3}{(n+4)^3+(n+5)^3} =\left[\frac{\infty}{\infty}\right] =\lim_{n\to\infty}\frac{\frac{(n+1)^3}{n^3}+\frac{(n+2)^3}{n^3}}{\frac{(n+4)^3}{n^3}+\frac{(n+5)^3}{n^3}} =\lim_{n\to\infty}\frac{\left(1+\frac{1}{n}\right)^3+\left(1+\frac{2}{n}\right)^3}{\left(1+\frac{4}{n}\right)^3+\left(1+\frac{5}{n}\right)^3} =\frac{2}{2} =1 \]