[math-fun] Puzzle about polynomial roots

For n >= 1 let E_n(z) = 1 + z + z^2/2! + ... + z^n/n!, the truncated series for exp(z). Let {r(n,1),...,r(n,n)} be the set of roots of E_n(z). (It's easy to verify there are no repeated roots.) Puzzle: Find the limit as n -> oo of sum from k = 1 to n of 1/(E_n)'(r(n,k)). --Dan