1/3*1+1/4*2+1/5*3+1/6*4+.+1/1999*1997+1/2000*1998怎么算?

1/3*1+1/4*2+1/5*3+1/6*4+.+1/1999*1997+1/2000*1998怎么算?
1/3*1+1/4*2+1/5*3+1/6*4+.+1/1999*1997+1/2000*1998怎么算?

1/3*1+1/4*2+1/5*3+1/6*4+.+1/1999*1997+1/2000*1998怎么算?
=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/1997-1/1999+1/1998-1/2000)
=1/2*(1+1/2-1/1999-1/2000)
=5993001/7996000

1/(3×1)+1/(4×2)+1/(5×3)+...+1/(2000×1998)
=(1/2)(1-1/3+1/2-1/4+1/3-1/5+...+1/1998-1/2000)
=(1/2)[(1+1/2+1/3+...+1/1998)-(1/3+1/4+1/5+...+1/1998+1/1999+1/2000)]
=(1/2)(1+1/2-1/1999-1/2000)
=5993001/7996000