[math-fun] Sequence of polynomials with largest real root approaching e?

Is there a sequence of polynomials p_n(x) such that p_n(x) is degree n p_{n+1}(x) = p_n(x) + k_n and the largest root of p_n approaches e as n -> infinity? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com