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42
I know it's only Power Mean but bear with me.. [ILL 1971]
I know it's only Power Mean but bear with me.. [ILL 1971]
Source:
January 1, 2011
inequalities
induction
inequalities proposed
Problem Statement
Show that for nonnegative real numbers
a
,
b
a,b
a
,
b
and integers
n
≥
2
n\ge 2
n
≥
2
,
a
n
+
b
n
2
≥
(
a
+
b
2
)
n
\frac{a^n+b^n}{2}\ge\left(\frac{a+b}{2}\right)^n
2
a
n
+
b
n
≥
(
2
a
+
b
)
n
When does equality hold?
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