Putnam 1975 B6

B-6. Show that if $s_{n}=1+\frac{1}{2}+\frac{1}{3}+\cdots+1 / n$, then (a) $n(n+1)^{1 / n}<n+s_{n}$ for $n>1$, and (b) $(n-1) n^{-1 /(n-1)}<n-s_{n}$ for $n>2$.