Problem #$10$: Which $of$ the following sequences converge?

$(i)a_n=\frac{(-1{)}^{n+1}n}{n^2+3}$

$(ii)a_n=\frac{(-1{)}^{n+1}{n}^2}{n^2-9}$

$(iii)a_n=cos[(2n-1)\frac{}{2}]$

$(iv)a_n=sin[(2n-1)\frac{}{2}]$

$(A)(ii)$ and $(iv)$ only

$(B)$ all $of$ them

$(C)$ none $of$ them

$(D)(i)$ and $(iv)$ only

$(E)(ii)$ and $(iii)$ only

$(F)(ii)$ only

$(G)(i)$ only $(H)(i)$ and $(iii)$ only

Problem #$10$:

Submit Problem #$10$ for Grading