Which of the following sequences (left(a_{n} ight)) are convergent and which are not? For the convergent sequences,

Which of the following sequences \(\left(a_{n}\right)\) are convergent and which are not? For the convergent sequences, find the limit.

(i) \(a_{n}=\frac{n}{n+5}\).

(ii) \(a_{n}=\frac{1}{\sqrt{n+5}}\).

(iii) \(a_{n}=\frac{n \sqrt{n}}{n+5}\).

(iv) \(a_{n}=\frac{(-1)^{n} \sin n}{\sqrt{n}}\).

(v) \(a_{n}=\frac{n^{3}-2 \sqrt{n}+7}{2-n^{2}-5 n^{3}}\).

(vi) \(a_{n}=\frac{1-(-1)^{n} n}{n}\).

(vii) \(a_{n}=\sqrt{n+1}-\sqrt{n}\).