IMO Shortlist 1966 problem 30
Dodao/la:
arhiva2. travnja 2012. Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a positive integer, prove that :
(a)
![\log_{10}(n + 1) > \frac{3}{10n} +\log_{10}n ;](/media/m/2/b/c/2bcc6c82d80846a9f9fe7723cc2b0764.png)
(b)
%V0
Let $n$ be a positive integer, prove that :
(a) $\log_{10}(n + 1) > \frac{3}{10n} +\log_{10}n ;$
(b) $\log n! > \frac{3n}{10}\left( \frac 12+\frac 13 +\cdots +\frac 1n -1\right).$
Izvor: Međunarodna matematička olimpijada, shortlist 1966