`A=(2)/(1.5)+(3)/(5.11)+(4)/(11.19)+(5)/(19.29)+(6)/(29.41)`
`=>2A=(4)/(1.5)+(6)/(5.11)+(8)/(11.19)+(10)/(19.29)+(12)/(29.41)`
`=>2A=1-(1)/(5)+(1)/(5)-(1)/(11)+(1)/(11)-(1)/(19)+(1)/(19)-(1)/(29)+(1)/(29)-(1)/(41)`
`=>2A=1-(1)/(41)=40/41`
`=>A=20/41`
``
`B=(1)/(1.4)+(2)/(4.10)+(3)/(10.19)+(4)/(19.31)`
`=>3B=(3)/(1.4)+(6)/(4.10)+(9)/(10.19)+(12)/(19.31)`
`=>3B=1-(1)/(4)+(1)/(4)-(1)/(10)+(1)/(10)-(1)/(19)+(1)/(19)-(1)/(31)`
`=>3B=1-(1)/(31)=(30)/(31)`
`=>B=10/31`
Vì : `(20)/(41)>(10)/(31)=>A>B`
\(A=\dfrac{2}{1.5}+\dfrac{3}{5.11}+...+\dfrac{6}{29.41}\)
\(2A=\dfrac{4}{1.5}+\dfrac{6}{5.11}+...+\dfrac{12}{29.41}\)
\(2A=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{29}-\dfrac{1}{41}=1-\dfrac{1}{41}=\dfrac{40}{41}\)
\(\Rightarrow A=\dfrac{40}{41}:2=\dfrac{20}{41}\)
\(B=\dfrac{1}{1.4}+\dfrac{2}{4.10}+...+\dfrac{4}{19.31}\)
\(3B=\dfrac{3}{1.4}+\dfrac{6}{4.10}+...+\dfrac{12}{19.31}\)
\(3B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{10}+...+\dfrac{1}{19}-\dfrac{1}{31}=1-\dfrac{1}{31}=\dfrac{30}{31}\)
\(\Rightarrow B=\dfrac{30}{31}:3=\dfrac{10}{31}\)
\(\Rightarrow A=\dfrac{20}{41}>B=\dfrac{10}{31}\)