Supp guys...I've got a serie I don't know how to find its limit, nor the sum!
If you could help me I would appreciate!
Here it is:
As with all series, you should start by asking yourself approximately how large is the n'th term of the series. In this case, for large values of n, $\displaystyle \frac{\sqrt n+1}{\sqrt[3]{n^5}}$ is approximately $\displaystyle \frac{n^{1/2}}{n^{3/5}} = n^{-1/10}$. Then $\displaystyle \textstyle 1-\cos(n^{-1/10})\approx \frac12n^{-1/5}$ (from the power series expansion of cos). So the series diverges, by comparison with $\displaystyle \textstyle\sum n^{-1/5}$.