Question

cho \(A=\frac{196}{197}+\frac{197}{198}=\frac{196+197}{197+198}\)so sánh A và B

Answer 1

Ta có:

\(\frac{196}{197+198}<\frac{196}{197}\)

\(\frac{197}{197+198}<\frac{197}{198}\)

\(\Rightarrow\frac{196}{197+198}+\frac{197}{197+198}<\frac{196}{197}+\frac{197}{198}\left(1\right)\)

Mà \(B=\frac{196+197}{197+198}=\frac{196}{197+198}+\frac{197}{197+198}\left(2\right)\)

Từ ( 1 ) và ( 2 )

\(\Rightarrow B<\frac{196}{197}+\frac{197}{198}\)

\(\Rightarrow B

Answer 2

Gọi 196/197 là a/c, 197/198 la b/d

Có a/c+b/d=a+b/c+d( tính chất của dãy tỉ số bằng nhau)

Answer 3

\(A=\frac{196}{197}+\frac{197}{198}\)            \(B=\frac{196+197}{197+198}\)          

 \(A=\frac{196}{197}+\frac{197}{198}\)           \(B=\frac{196}{197+198}+\frac{197}{197+198}\)

Ta có: \(\frac{196}{197}>\frac{196}{197+198}\) vì \(197<197+198\)

         \(\frac{197}{198}>\frac{197}{197+198}\) vì \(198<197+198\)

\(\Rightarrow\)\(\frac{196}{197}+\frac{197}{198}\)  \(>\frac{196}{197+198}+\frac{197}{197+198}\)

\(\Leftrightarrow\)\(\frac{196}{197}+\frac{197}{198}\)\(>\)\(\frac{196+197}{197+198}\)

Vậy \(A>B\)