Let $\left \{ f_{n} \right \}^{\infty }_{n=1}$ be the sequence of functions on $\mathbb{R}$ defined by $f_{n}\left ( x \right )=n^{2}x^{n}.$. Let $A$ be the set of all points $a$ in $\mathbb{R}$ such that the sequence $\left \{ f_{n} \left ( a \right )\right \}^{\infty }_{n=1}$ converges. Then
- $A=\left \{0\right \}$
- $A=\left [0,1\right )$
- $A=\mathbb{R}\setminus \left \{-1,1\right \}$
- $A=\left (-1,1\right ).$
