Question

Cho A =\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+........+\frac{1}{29}+\frac{1}{30}.\) . Hãy so sánh A với \(\frac{5}{6}\)

Giúp với, cần gấp 

Ai trả lời nhanh mik cho 3 tick

PS:Làm cả bài giải luôn nhé!!!!>.< 

Answer 1

\(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{29}+\frac{1}{30}\)

\(A=\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\right)+\left(\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{30}\right)\)

\(A>\left(\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\right)+\left(\frac{1}{30}+\frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}\right)\)

\(A>10.\frac{1}{20}+10.\frac{1}{30}\)

\(A>\frac{1}{2}+\frac{1}{3}\)

\(A>\frac{5}{6}\)

Vậy \(A>\frac{5}{6}\)

Chúc bạn học tốt ~ 

Answer 2

\(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{29}+\frac{1}{30}\)

\(A=\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\right)+\left(\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{30}\right)\)

\(A>\left(\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\right)+\left(\frac{1}{30}+\frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}\right)\)

\(A>\frac{1}{20}\times10+\frac{1}{30}\times10\)

\(A>\frac{1}{2}+\frac{1}{3}\)

\(A>\frac{5}{6}\)

Vậy \(A>\frac{5}{6}\)