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1/1*2+1/2*3+1/3*4······+1/2013*2014

=1-1/2+1/2-1/3+1/3-1/4+...+1/2014-1/2015 =1-1/2015 =2014/2015

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200) =1/3+1/6+1/10+.........+1/[(1+200)*200/2] =1/3+1/6+1/10+.........+1/20100 =2(1/6+1/12+1/20+.........+1/40200) =2(1/2-1/3+1/3-1/4+1/4-1/5+.....+1/200-1/201) =2×(...

=1/2-1/3+1/3-1/4+1/4-1/5……+1/98-1/99+1/99-1/100 =1/2-1/100 =49/100 当然是我了

原题=99x1/2x2/3x3/4……97/98x98/99 =99x1/99 =1

1/1+(2/1-1/2)+(3/1-2/2+1/3)+(4/1-3/2+2/3-1/4)+...+(9/1-8/2+7/3-6/4+5/5-4/6+3/7-2/8+1/9 =(1+2+......

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