Analysis Arithmetic series .Verify which of the following sequences converge. Verify which of the following sequences converge.$$1.A(n)=\sum_{n=1,n=+00}(1/(n^{1+1/n})$$  $$2. B(n)=(1/\sqrt{n^2+1})+.......n/\sqrt{n^2+n}$$ 
$$3.C(n)=(n+cos(n^2))/(n+sin(n)) $$ .For the 3th one cant i just take the absolute value  so $C(n)<=n+1/n-1$ ?? .For the first one i cant find a sequence to compare.And for the second one i say $B(n)<=n^2/\sqrt{n^2+n}<=n/\sqrt{1+1/n}$ but is not helping.

Edit:
Manoli, note that $n^{1/n} \lt 2$ for all $n$.
It follows that $\dfrac{1}{n^{1+1/n}}\gt \dfrac{1}{2n}$. 
$$\sum_{n=1}^{\infty} \frac{1}{2n} \text{diverges}$$
so $\sum_{n=1}^{\infty} \frac{1}{n^{1+\frac{1}{n}}}$ also diverges.
