MathDB
b(n,0) - b(n,1) x +b(n,2) x^2 - ... + (-1)^k b(n,k) x^k > 0$

Source: Eotvos 1929 p2

September 10, 2024
Binomialbinomial coefficientsalgebrainequalities

Problem Statement

Let k≤nk \le n be positive integers and xx be a real number with 0≤x<1/n0 \le x < 1/n. Prove that (n0)−(n1)x+(n2)x2−...+(−1)k(nk)xk>0{n \choose 0} - {n \choose 1} x +{n \choose 2} x^2 - ... + (-1)^k {n \choose k} x^k > 0
Back to ProblemsView on AoPS