Lời giải:
Ta có:
$S=\frac{5}{6!}+\frac{5}{7!}+\frac{5}{8!}+...+\frac{5}{91!}$
$<\frac{5}{6!}+85.\frac{5}{91!}$
Mà $\frac{5}{6!}+85.\frac{5}{91!}<\frac{1}{5!}$
$=>S=\frac{5}{6!}+\frac{5}{7!}+\frac{5}{8!}+...+\frac{5}{91!}<\frac{1}{5!}(đpcm)$
Từ quy tắc:
$a+b+c+...+z<a+(z-a).z$
