Question

so sánh \(\frac{2000}{2001}+\frac{2002}{2003}\) và\(\frac{2000+2002}{2001+2003}\)

ghi cách làm zùm mik nha, giải bằng cách lớp 6

Answer 1

ta có \(\frac{2000+2002}{2001+2003}\)= \(\frac{2000}{2001+2003}\)+ \(\frac{2002}{2001+2003}\)=\(\frac{2000}{4004}\)+\(\frac{2002}{4004}\)

ta có \(\frac{2000}{2001}\)>\(\frac{2000}{4004}\) và \(\frac{2002}{2003}\)> \(\frac{2002}{4004}\)

 nên \(\frac{2000}{2001}\)+\(\frac{2002}{2003}\)>\(\frac{2000}{4004}\)+\(\frac{2002}{4004}\)

vậy \(\frac{2000}{2001}\)+\(\frac{2002}{2003}\)>\(\frac{2000+2002}{2001+2003}\)

Answer 2

\(\frac{2000+2002}{2001+2003}=\frac{2000}{2001+2003}+\frac{2002}{2001+2003}< \frac{2000}{2001}+\frac{2002}{2003}\)