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Natural numbers/Induction/Product of powers/Exercise
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Natural numbers
Prove, by induction, that the following inequality holds
1
⋅
2
2
⋅
3
3
⋯
n
n
≤
n
n
(
n
+
1
)
2
.
{\displaystyle {}1\cdot 2^{2}\cdot 3^{3}\cdots n^{n}\leq n^{\frac {n(n+1)}{2}}\,.}
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