Let f : [0, 1] → [1, ∞) be defined by \(\rm f(x)=\frac{1}{1-x}\), For n ≥ 1, let pn(x) = 1 + x + ....+ xn, Then which of the following statements are true?
1
f(x) is not uniformly continuous on [0, 1)
2
The sequence (pn(x)) converges to f(x) pointwise on [0, 1)
3
The sequence (pn(x)) converges to f(x) uniformly on [0, 1)
4
The sequence (pn(x)) converges to f(x) uniformly on [0, c| for every 0 < c < 1