Mind the Research

IBM Research | Ponder This

Ponder This Challenge: This month's puzzle was submitted by Peter Beech.

For n>1 let P(x)= 1 + x1/1! + x2/2! + ... + xn/n! be the polynomial of degree n formed from the first n+1 terms of the power series for ex. When n is odd, this polynomial has one real root. Prove that this root is irrational for all odd n>1.