Error in Taylor Approximations

f[x_] := (E^x)

p[n_,x_] := 1 + (∑_(i=1)^n)((x^i)/(i!))

e[n_,x_] := f[x] - p[n,x]

e[2,0]

N[e[2,2]]

Plot[e[n,2],{n,2,10}]

N[e[10,2]]