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((a+1)/(b+1))^(b+1) >=(a/b)^b for a,b>0

Source: 1984 Swedish Mathematical Competition p3

March 28, 2021

algebrainequalities

Problem Statement

Prove that if

a,b

are positive numbers, then

\left( \frac{a+1}{b+1}\right)^{b+1} \ge \left( \frac{a}{b}\right)^{b}