MathDB

5

Part of 1984 National High School Mathematics League

Problems(2)

Odd Funcion or Not?

Source: 1984 National High School Mathematics League, Exam One, Problem 5

2/22/2020
If a>0,a≠1a>0,a\neq1, F(x)F(x) is an odd function. G(x)=F(x)⋅(1ax−1+12)G(x)=F(x)\cdot(\frac{1}{a^x-1}+\frac{1}{2}), then G(x)G(x) is (A)\text{(A)} odd function (B)\text{(B)} even function (C)\text{(C)} not odd or even function (D)\text{(D)} not sure
function
Maybe the Easiest Inequality You've Seen!

Source: 1984 National High School Mathematics League, Exam Two, Problem 5

2/22/2020
x1,x2,⋯ ,xnx_1,x_2,\cdots,x_n are positive real numbers. Prove that x12x2+x22x3+⋯+xn2x1≥x1+x2+⋯xn.\frac{x_1^2}{x_2}+\frac{x_2^2}{x_3}+\cdots+\frac{x_n^2}{x_1}\geq x_1+x_2+\cdots x_n.
inequalities