Question

Cho Q=\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{89}+\frac{1}{90}.\)

So sánh Q với \(\frac{5}{6}.\)

Các bạn giải ra hộ mình nhé!

Answer 1

Đặt  \(A=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{60}>\frac{1}{60}+\frac{1}{60}+\frac{1}{60}+...+\frac{1}{60}=30.\frac{1}{60}=\frac{1}{2}\)

       \(B=\frac{1}{61}+\frac{1}{62}+\frac{1}{63}+...+\frac{1}{90}>\frac{1}{90}+\frac{1}{90}+\frac{1}{90}+...+\frac{1}{90}=30.\frac{1}{90}=\frac{1}{3}\)

\(=>Q=\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{90}=A+B>\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\)

Vậy \(Q>\frac{5}{6}\)