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Common Inequalities
Common Inequalities
3 questions
Difficulty 2-3
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Foundation
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foundation (2/10)
state theorem
The AM-GM inequality states that for non-negative reals
a
1
,
…
,
a
n
, the arithmetic mean is at least the geometric mean. Which is the correct statement?
Hide and think first
A.
a
1
+
a
2
+
⋯
+
a
n
≥
n
⋅
n
a
1
a
2
⋯
a
n
with no equality condition specified
B.
n
a
1
+
a
2
+
⋯
+
a
n
≤
n
a
1
a
2
⋯
a
n
with equality iff one term is zero
C.
n
a
1
+
a
2
+
⋯
+
a
n
≥
n
a
1
a
2
⋯
a
n
with equality iff all
a
i
are equal
D.
n
a
1
2
+
a
2
2
+
⋯
+
a
n
2
≥
n
a
1
a
2
⋯
a
n
holds without restrictions on the signs
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