Question

Cho a; b; c; d \(\inℕ^∗\)thỏa mãn \(\frac{a}{b}< \frac{c}{d}\). Chứng minh rằng: \(\frac{2018a+c}{2018b+d}< \frac{c}{d}\)

Giúp với!!!

Khẩn cấp!!!

Ai nhanh cho 3 tích

Answer 1

Ta có: \(\frac{a}{b}< \frac{c}{d}\Leftrightarrow ad< bc\)

\(\Leftrightarrow2018ad< 2018bc\)

\(\Leftrightarrow2018ad+cd< 2018bc+cd\)

\(\Leftrightarrow d\left(2018a+c\right)< c\left(2018b+d\right)\)

\(\Leftrightarrow\frac{2018a+c}{2018b+d}< \frac{c}{d}\left(đpcm\right)\)

Answer 2

ta có a/b < c/d 

=> ad<bc 

=> 2018ad < 2018bc

=> 2018ad + cd < 2018bc + cd 

=> ( 2018 a + c ) < c ( 2018 b + d )

=> \(\frac{2018a+c}{2018b+d}< \frac{c}{d}\left(\text{đ}pcm\right)\)