CHÚC MỪNG NĂM MỚI.
Cho:A=1/1999+2/1998+3/1997+4/1996+. . . . .+1998/2+1999/1
B= 1/2+1/3+1/4+1/5+.....+1/2000
Rút gọn: A/B=?
Bài giải
Ta có:
A=1/1999+2/1998+....+1998/2+1999/1
→A+1999=
=(1/1999+1)+(2/1998+1)+...+(19998/2+1)…
(1999/1+1)
=2000/1999+2000/1998+...+2000/2+2000/1
=2000(1/2+1/3+...+1/1999)+2000
→A=2000(1/2+1/3+...+1/2000)
=2000.B
→A/B=2000