24) Вычислить: 1) \(\lim_{n\to\infty}\frac{3-2^n}{2^n}\); 2) \(\lim_{n\to\infty}\frac{3^{n+2}+2}{3^n}\); 3) \(\lim_{n\to\infty}\frac{(5^n+1)^2}{5^{2n}}\).

1. \(\displaystyle\frac{3-2^n}{2^n}=\frac3{2^n}-1\to-1\).
2. \(\displaystyle\frac{3^{n+2}+2}{3^n}=9+\frac2{3^n}\to9\).
3. \(\displaystyle\frac{(5^n+1)^2}{5^{2n}}=\left(1+\frac1{5^n}\right)^2\to1\).

Ответ: 1) −1; 2) 9; 3) 1.