1/3*1+1/4*2+1/5*3+1/6*4+.+1/1999*1997+1/2000*1998怎么算?
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![1/3*1+1/4*2+1/5*3+1/6*4+.+1/1999*1997+1/2000*1998怎么算?](/uploads/image/z/128375-71-5.jpg?t=1%2F3%2A1%2B1%2F4%2A2%2B1%2F5%2A3%2B1%2F6%2A4%2B.%2B1%2F1999%2A1997%2B1%2F2000%2A1998%E6%80%8E%E4%B9%88%E7%AE%97%3F)
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