Question

[Long ma Bắc Giang]

Giúp tui:

Cho $A=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+\mathrm{...}+\frac{1}{59}+\frac{1}{60}$. Chứng minh $A<\frac{4}{5}.$

Answer 1

[Akai Haruma]

Lời giải:

$A=(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{39})+(\frac{1}{40}+\frac{1}{41}+....+\frac{1}{49})+(\frac{1}{50}+....+\frac{1}{59})+\frac{1}{60}$

$< \frac{9}{30}+\frac{10}{40}+\frac{10}{50}+\frac{1}{60}=\frac{23}{30}< \frac{4}{5}$