Question

So sanh \(A=\frac{1}{42}+\frac{1}{43}+.......+\frac{1}{80}\)va \(B=\frac{7}{12}\)

Answer 1

Ta có

\(\frac{7}{12}=\frac{3}{12}+\frac{4}{12}=\frac{1}{4}+\frac{1}{3}=\frac{20}{80}+\frac{20}{60}=\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+...+\frac{1}{80}\)

\(>\frac{1}{42}+\frac{1}{43}+...+\frac{1}{80}\)

hay B>A

nhớ tick mình nha

Answer 2

Ta chia A làm hai phần mỗi phần 20 số hạng 

\(C=\frac{1}{41}+\frac{1}{42}+...+\frac{1}{60}\)với \(D=\frac{1}{61}+\frac{1}{62}+...+\frac{1}{80}\)

Xét \(C=\frac{1}{41}+\frac{1}{42}+...+\frac{1}{61}\)\(>\frac{1}{61}+\frac{1}{61}+\frac{1}{61}+...+\frac{1}{61}\)\(=\frac{1}{61}.20=\frac{1}{3}\)

Xét \(D=\frac{1}{61}+\frac{1}{62}+...+\frac{1}{80}>\frac{1}{80}+\frac{1}{80}+...+\frac{1}{80}=\frac{1}{80}.20=\frac{1}{4}\)

Mà A = C + D > \(\frac{1}{3}+\frac{1}{4}=\frac{7}{12}\)

=> A > B