Smooth normal computing

Hi, here is my issue :
Consider 5 vertices :
A( 0., 0., 0. ),
B( 0., 0., 1. ),
C( 1., 0., 1. ),
D( 1., 0., 0. ),
E( 1., -1., 1. );

with 3 faces :
1 : A, B, C
2 : A, C, D
3 : B, E, C

If these free faces are in the same smoothing group,
could you explain me how to compute the correct normal at the C point ?
Algorithm i saw run through faces and sum face normal to the vertex normal.
Then apply a division to mean and finally normalization.

Two questions :
1) Isn't the division useless ???
2) considering the exemple above, using this algorithm, the normal at the C point will be :

Nc = N1( 0., 1., 0. ) + N2( 0., 1., 0. ) + N3( 0., 0., 1. )
= N( 0., 2., 1. ).Normalize()

why did I expect my normal to be :
Nc = N( 0., 1., 1. ).Normalize()

Apologize my engl,
feel free to answer
thx