> 
> Evaluate
>  $$\lim\_{n\to\infty} \sum\_{m=1}^n \left(\left({1+\frac{m^3}{n^4}}\right)^{1/8}-1\right).$$
> 
> 
> 

All I can say it's goes to indefinity $\infty-\infty$ so I'm interested in general idea rather than an exact answer.