Đáp án:
`B = (196 + 197)/(197 + 198)`
`⇔ B = 196/(197 + 198) + 197/(197 + 198)`
Ta thấy : \(\left\{ \begin{array}{l}197 < 197 + 198\\198 < 197 + 198\end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}\dfrac{1}{197} > \dfrac{1}{197 + 198}\\ \dfrac{1}{198} > \dfrac{1}{197 + 198}\end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}196 × \dfrac{1}{197} > 196 × \dfrac{1}{197 + 198}\\197×\dfrac{1}{198} > 197×\dfrac{1}{197 + 198} \end{array} \right.\)
`⇔` \(\left\{ \begin{array}{l}\dfrac{196}{197} > \dfrac{196}{197 + 198}\\ \dfrac{197}{198} > \dfrac{197}{197 + 198}\end{array} \right.\)
Cộng theo vế ta được :
`⇔ 196/197 + 197/198 > 196/(197 + 198) + 197/(197 + 198)`
`⇔ 196/197 + 197/198 >(196 + 197)/(197 + 198)`
`⇔ A > B`
Vậy `A > B`
