Question 30
(ROM) If $n$ is a natural number, prove that
(a) $\log_{10}(n+1)>\frac3{10n}+\log_{10}n$;
(b) $\log n!>\frac{3n}{10}\left(\frac12+\frac13+\cdots+\frac1n-1\right)$.
(a) $\log_{10}(n+1)>\frac3{10n}+\log_{10}n$;
(b) $\log n!>\frac{3n}{10}\left(\frac12+\frac13+\cdots+\frac1n-1\right)$.