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Swedish Mathematical Competition
1984 Swedish Mathematical Competition
3
3
Part of
1984 Swedish Mathematical Competition
Problems
(1)
((a+1)/(b+1))^(b+1) >=(a/b)^b for a,b>0
Source: 1984 Swedish Mathematical Competition p3
3/28/2021
Prove that if
a
,
b
a,b
a
,
b
are positive numbers, then
(
a
+
1
b
+
1
)
b
+
1
≥
(
a
b
)
b
\left( \frac{a+1}{b+1}\right)^{b+1} \ge \left( \frac{a}{b}\right)^{b}
(
b
+
1
a
+
1
)
b
+
1
≥
(
b
a
)
b
algebra
inequalities