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IMO Shortlist 1966 problem 30
1966
shortlist
Let
be a positive integer, prove that :
(a)
(b)
%V0 Let $n$ be a positive integer, prove that : (a) $\log_{10}(n + 1) > \frac{3}{10n} +\log_{10}n ;$ (b) $\log n! > \frac{3n}{10}\left( \frac 12+\frac 13 +\cdots +\frac 1n -1\right).$
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IMO Shortlist 1966 problem 42
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