Conventions
|E| is the magnitude of vector E.
all limits are as n approaches infinity
ln e = 1
The power series 1 + x + x^2 + x^3 + ... + x^n diverges when
x>=1 and has the root,
x = lim ln[(n!(n+1)|E|^2 - n!e^2)/(n!e-(n+1))]
where \
|E|^2=(1/0!)^2 + (1/1!)^2 + (1/2!)^2 + (1/3!)^2 + ... + (1/n!)^2
Proof
1+lim{(1+2+3+...+n)ln[(n!(n+1)|E|^2 - n!e^2)/(n!e-(n+1))]=0
lim ln[(n!(n+1)|E|^2 - n!e^2)/(n!e-(n+1))]=-lim 1/(1+2+3+...+n)=0
lim [(n!(n+1)|E|^2 - n!e^2)/(n!e-(n+1))]=1
lim 1/(n!e-(n+1)) = lim 1/(n!(n+1)|E|^2 - n!e^2)
0=0
E.O.P.
