Showing that a set is not closed Let $C$ be the set of continuous real valued functions on $[0,1]$ with metric    
$$d(f,g) = \text{sup} \{ |f(x) - g(x)| \ : x \in \ [0,1]\}$$     
Show that the set of Polynomials in $C$ is not closed. 
I don't know how to approach this problem.   
Please help.
Thanks in advance.

Take the sequence of polynomials given by
$$
1\\
1+x\\
1+x+\frac12x^2\\
1+x+\frac12x^2+\frac16x^3\\
\vdots\\
1+x+\frac12x^2+\cdots+\frac1{n!}x^n\\
\vdots
$$
Does this sequence converge to an element of $C$? Does it converge to a polynomial?
