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1987 All Soviet Union Mathematical Olympiad
462
ASU 462 All Soviet Union MO 1987 (2n + 1)^n >= (2n)^n + (2n - 1)^n
ASU 462 All Soviet Union MO 1987 (2n + 1)^n >= (2n)^n + (2n - 1)^n
Source:
August 7, 2019
algebra
inequalities
Problem Statement
Prove that for every natural
n
n
n
the following inequality is held:
(
2
n
+
1
)
n
≥
(
2
n
)
n
+
(
2
n
−
1
)
n
(2n + 1)^n \ge (2n)^n + (2n - 1)^n
(
2
n
+
1
)
n
≥
(
2
n
)
n
+
(
2
n
−
1
)
n
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