IBM Ponder This #065 · September 2003

This month's puzzle was submitted by Peter Beech.

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

Solution

Best opened after a real attempt

To be added.