MathDB

1. Let

a_{v}

and

b_{v}

{v= 1,2,\dots,n}

, be real numbers such that

a_{1}\geq a_{2} \geq a_{3}\geq\dots\geq a_{n}> 0

and

b_{1}\geq a_{1}, b_{1}b_{2}\geq a_{1}a_{2},\dots,b_{1}b_{2}\dots b_{n}\geq a_{1}a_{2}\dots a_{n}

Show that

b_{1}+b_{2}+\dots+b_{n}\geq a_{1}+a_{2}+\dots+a_{n}

(S. 4)

Problem Statement