$\lim_{n\rightarrow\infty}\frac{5n}{n^3-2}$  

 $\lim_{n\rightarrow\infty}\frac{4n^2-8n+100}{1000-11n\ -2n^2}$ 

 $\lim_{n\rightarrow\infty}\frac{\left(n+100\right)^{500}}{\left(n-100\right)^{700}}$ 

 $\lim_{n\rightarrow\infty}\frac{\sqrt{9n^2+1}}{n}$ 

 $\lim_{n\rightarrow\infty}\frac{\sqrt{1+n^2}\left(n^2+2n-1\right)^5}{5n^{11}+1}$ 

 $\lim_{n\rightarrow\infty}\frac{1+10^n}{1-10^n}$ 

 $\lim_{n\rightarrow\infty}\frac{2^n+3^n}{5^n}$  

 $\lim_{x\rightarrow\infty}\left(5+\frac{1}{x}\right)$  

 $a_n=\left(-\frac{1}{2}\right)^n$ is convergent sequence /or/ divergent sequence ?